[Introduction] - Groups of Genus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Congruence Subgroups of PSL(2,Z) of Genus 6

Groups of Level: 10 11 14 16 17 18 20 21 22 24 25 27 28 30 31 32 35 36 39 42 44 45 48 50 52 54 56 58 60 63 64 66 69 70 71 72 75 76 77 78 79 84 86 87 90 91 100 105 108 121 125 126
 
 
^ Level 10 Name Index  con   len   c2   c3  > SL(2,Z/10Z) Matrix Generators
  10A6 180 1 45 4 0 [ 7, 4, 5, 3 ] , [ 9, 0, 0, 9 ]
^ Level 11 Name Index  con   len   c2   c3  > SL(2,Z/11Z) Matrix Generators
  11A6 132 1 66 0 0 [ 3, 6, 9, 0 ] , [ 10, 0, 0, 10 ]
^ Level 14 Name Index  con   len   c2   c3  > SL(2,Z/14Z) Matrix Generators
  14A6 126 2 63 4 0 [ 1, 12, 1, 13 ] , [ 5, 8, 2, 9 ] , [ 7, 2, 10, 7 ] , [ 13, 0, 0, 13 ]
  14B6 168 1 168 8 3 [ 11, 5, 7, 2 ] , [ 13, 0, 0, 13 ] , [ 13, 2, 13, 1 ]
^ Level 16 Name Index  con   len   c2   c3  > SL(2,Z/16Z) Matrix Generators
  16A6 96 1 4 0 0 [ 1, 8, 8, 1 ] , [ 9, 4, 12, 9 ] , [ 9, 8, 0, 9 ] , [ 11, 8, 12, 3 ] , [ 13, 4, 8, 5 ] , [ 15, 8, 8, 15 ]
  16B6 96 1 24 0 0 [ 1, 8, 8, 1 ] , [ 4, 15, 1, 0 ] , [ 9, 4, 4, 9 ] , [ 9, 8, 0, 9 ] , [ 9, 12, 12, 9 ] , [ 15, 8, 8, 15 ]
  16C6 192 1 48 4 0 [ 0, 1, 15, 0 ] , [ 1, 0, 8, 1 ] , [ 1, 8, 8, 1 ] , [ 8, 15, 1, 8 ] , [ 15, 0, 0, 15 ] , [ 15, 8, 8, 15 ]
^ Level 17 Name Index  con   len   c2   c3  > SL(2,Z/17Z) Matrix Generators
  17A6 136 1 136 8 1 [ 3, 11, 13, 14 ] , [ 4, 11, 15, 16 ] , [ 12, 3, 1, 6 ] , [ 16, 0, 0, 16 ]
^ Level 18 Name Index  con   len   c2   c3  > SL(2,Z/18Z) Matrix Generators
  18A6 108 1 9 0 0 [ 1, 0, 9, 1 ] , [ 1, 6, 12, 1 ] , [ 7, 6, 0, 13 ] , [ 17, 0, 0, 17 ]
  18B6 108 1 27 4 0 [ 1, 17, 8, 11 ] , [ 2, 15, 15, 5 ] , [ 10, 9, 9, 1 ] , [ 13, 15, 15, 16 ]
  18C6 108 1 108 4 0 [ 1, 12, 6, 1 ] , [ 3, 4, 11, 3 ] , [ 13, 9, 9, 16 ] , [ 17, 6, 12, 17 ]
  18D6 108 2 27 4 0 [ 5, 0, 12, 11 ] , [ 7, 12, 0, 13 ] , [ 13, 0, 6, 7 ] , [ 15, 10, 17, 15 ]
  18E6 108 2 54 4 0 [ 1, 16, 1, 17 ] , [ 7, 3, 3, 4 ] , [ 16, 9, 9, 13 ] , [ 17, 0, 0, 17 ]
^ Level 20 Name Index  con   len   c2   c3  > SL(2,Z/20Z) Matrix Generators
  20A6 120 1 40 0 6 [ 5, 17, 17, 14 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 0, 11 ] , [ 13, 0, 8, 17 ] , [ 17, 16, 0, 13 ]
  20B6 120 1 60 8 0 [ 6, 15, 15, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 12, 4, 1 ] , [ 11, 0, 0, 11 ] , [ 12, 15, 17, 8 ]
  20C6 120 1 120 0 6 [ 7, 0, 2, 3 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 0, 11 ] , [ 11, 9, 3, 8 ] , [ 17, 6, 10, 13 ]
  20D6 180 1 45 4 0 [ 1, 0, 10, 1 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 5, 11 ] , [ 11, 0, 10, 11 ] , [ 17, 14, 5, 3 ]
^ Level 21 Name Index  con   len   c2   c3  > SL(2,Z/21Z) Matrix Generators
  21A6 84 2 7 0 0 [ 1, 18, 3, 13 ] , [ 4, 6, 3, 10 ] , [ 7, 18, 12, 7 ] , [ 8, 0, 0, 8 ] , [ 13, 0, 0, 13 ] , [ 13, 6, 15, 7 ]
  21B6 112 1 112 0 1 [ 1, 7, 14, 15 ] , [ 1, 18, 3, 13 ] , [ 8, 14, 7, 15 ] , [ 13, 0, 0, 13 ] , [ 13, 6, 15, 7 ] , [ 15, 4, 17, 20 ] , [ 15, 14, 7, 1 ]
  21C6 126 1 63 10 0 [ 7, 18, 12, 7 ] , [ 8, 0, 0, 8 ] , [ 8, 14, 14, 1 ] , [ 13, 0, 0, 13 ] , [ 19, 6, 18, 19 ] , [ 19, 9, 15, 16 ]
^ Level 22 Name Index  con   len   c2   c3  > SL(2,Z/22Z) Matrix Generators
  22A6 120 1 12 0 0 [ 1, 11, 11, 12 ] , [ 7, 4, 2, 17 ] , [ 7, 20, 10, 13 ] , [ 11, 14, 18, 13 ] , [ 16, 21, 5, 19 ]
  22B6 132 1 66 12 0 [ 5, 2, 9, 17 ] , [ 9, 10, 0, 5 ] , [ 12, 11, 11, 1 ] , [ 21, 0, 0, 21 ]
  22C6 Γ1(22) 180 1 36 0 0 [ 5, 10, 16, 19 ] , [ 7, 4, 2, 17 ] , [ 11, 14, 18, 13 ] , [ 12, 11, 11, 12 ] , [ 18, 9, 21, 2 ]
^ Level 24 Name Index  con   len   c2   c3  > SL(2,Z/24Z) Matrix Generators
  24A6 96 1 32 0 3 [ 1, 9, 5, 22 ] , [ 1, 16, 16, 17 ] , [ 9, 16, 8, 9 ] , [ 13, 0, 0, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 0, 19 ] , [ 22, 15, 19, 1 ]
  24B6 96 1 48 0 0 [ 1, 6, 3, 19 ] , [ 1, 12, 12, 1 ] , [ 1, 16, 0, 1 ] , [ 7, 12, 12, 7 ] , [ 13, 0, 12, 13 ] , [ 17, 4, 12, 17 ] , [ 17, 16, 0, 17 ] , [ 19, 0, 12, 19 ]
  24C6 96 1 96 0 3 [ 7, 0, 0, 7 ] , [ 13, 0, 0, 13 ] , [ 13, 4, 16, 5 ] , [ 17, 0, 0, 17 ] , [ 17, 4, 4, 1 ] , [ 22, 15, 19, 1 ]
  24D6 144 1 12 12 0 [ 7, 0, 0, 7 ] , [ 9, 8, 16, 9 ] , [ 9, 16, 8, 9 ] , [ 13, 12, 12, 13 ] , [ 16, 21, 3, 16 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 1 ]
  24E6 144 1 36 8 0 [ 1, 12, 0, 1 ] , [ 1, 12, 12, 1 ] , [ 7, 0, 0, 7 ] , [ 8, 13, 19, 16 ] , [ 13, 4, 16, 5 ] , [ 17, 0, 0, 17 ] , [ 23, 0, 0, 23 ]
  24F6 144 1 36 8 0 [ 1, 12, 0, 1 ] , [ 1, 12, 12, 1 ] , [ 7, 0, 0, 7 ] , [ 16, 1, 7, 20 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 1 ] , [ 23, 0, 0, 23 ]
  24G6 144 1 36 12 0 [ 7, 0, 0, 7 ] , [ 9, 4, 20, 9 ] , [ 13, 12, 12, 13 ] , [ 15, 4, 20, 15 ] , [ 15, 20, 4, 15 ] , [ 16, 21, 3, 16 ] , [ 17, 0, 0, 17 ] , [ 17, 8, 8, 1 ]
  24H6 144 1 36 12 0 [ 1, 0, 12, 1 ] , [ 1, 4, 22, 17 ] , [ 7, 0, 12, 7 ] , [ 7, 10, 7, 17 ] , [ 17, 0, 12, 17 ] , [ 19, 6, 9, 13 ] , [ 21, 8, 4, 21 ] , [ 23, 0, 0, 23 ]
  24I6 144 1 36 12 0 [ 1, 0, 12, 1 ] , [ 7, 0, 12, 7 ] , [ 7, 6, 9, 1 ] , [ 13, 4, 10, 5 ] , [ 17, 0, 12, 17 ] , [ 21, 8, 4, 21 ] , [ 23, 0, 0, 23 ]
  24J6 144 1 72 8 0 [ 5, 0, 0, 5 ] , [ 11, 12, 12, 11 ] , [ 13, 0, 12, 13 ] , [ 13, 12, 12, 13 ] , [ 13, 22, 7, 23 ] , [ 15, 8, 22, 15 ] , [ 19, 0, 0, 19 ] , [ 19, 12, 0, 19 ] , [ 23, 0, 0, 23 ]
  24K6 144 2 36 12 0 [ 1, 0, 12, 1 ] , [ 1, 20, 14, 17 ] , [ 3, 14, 1, 21 ] , [ 7, 0, 12, 7 ] , [ 9, 8, 16, 9 ] , [ 17, 0, 12, 17 ] , [ 19, 6, 9, 13 ] , [ 23, 0, 0, 23 ]
^ Level 25 Name Index  con   len   c2   c3  > SL(2,Z/25Z) Matrix Generators
  25A6 150 1 30 10 0 [ 3, 8, 5, 22 ] , [ 11, 5, 5, 16 ] , [ 18, 1, 1, 14 ] , [ 24, 0, 0, 24 ]
  25B6 150 1 30 10 0 [ 6, 15, 15, 21 ] , [ 6, 21, 16, 2 ] , [ 7, 23, 8, 5 ] , [ 19, 21, 3, 6 ]
  25C6 150 1 30 10 0 [ 4, 3, 11, 21 ] , [ 4, 15, 15, 19 ] , [ 9, 4, 19, 3 ] , [ 16, 20, 20, 11 ]
  25D6 150 1 30 10 0 [ 16, 20, 20, 11 ] , [ 17, 5, 17, 8 ] , [ 24, 0, 0, 24 ] , [ 24, 14, 9, 23 ]
  25E6 150 1 75 2 0 [ 1, 0, 15, 1 ] , [ 2, 14, 5, 23 ] , [ 11, 20, 15, 16 ] , [ 24, 0, 0, 24 ]
  25F6 150 1 75 2 0 [ 1, 5, 15, 1 ] , [ 2, 14, 5, 23 ] , [ 11, 0, 15, 16 ] , [ 24, 0, 0, 24 ]
^ Level 27 Name Index  con   len   c2   c3  > SL(2,Z/27Z) Matrix Generators
  27A6 108 1 36 0 3 [ 1, 0, 18, 1 ] , [ 1, 12, 2, 25 ] , [ 7, 24, 13, 10 ] , [ 19, 0, 0, 10 ] , [ 19, 0, 9, 10 ] , [ 26, 0, 0, 26 ]
^ Level 28 Name Index  con   len   c2   c3  > SL(2,Z/28Z) Matrix Generators
  28A6 84 2 21 0 0 [ 5, 22, 16, 9 ] , [ 9, 19, 24, 1 ] , [ 9, 20, 12, 5 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 0, 15 ] , [ 17, 24, 20, 25 ] , [ 21, 8, 20, 13 ] , [ 21, 12, 4, 21 ]
  28B6 84 2 21 0 0 [ 1, 14, 0, 1 ] , [ 5, 8, 16, 9 ] , [ 9, 12, 10, 1 ] , [ 9, 20, 12, 5 ] , [ 13, 0, 0, 13 ] , [ 13, 20, 8, 21 ] , [ 15, 14, 0, 15 ] , [ 21, 16, 24, 21 ]
  28C6 84 2 21 0 0 [ 1, 14, 0, 1 ] , [ 13, 0, 0, 13 ] , [ 13, 20, 8, 21 ] , [ 15, 14, 0, 15 ] , [ 21, 16, 24, 21 ] , [ 23, 26, 24, 15 ] , [ 25, 4, 8, 17 ]
  28D6 96 1 8 0 0 [ 1, 7, 7, 22 ] , [ 1, 14, 14, 1 ] , [ 9, 8, 26, 17 ] , [ 15, 0, 14, 15 ] , [ 25, 8, 12, 5 ]
  28E6 96 1 8 0 0 [ 5, 12, 12, 1 ] , [ 9, 12, 4, 21 ] , [ 13, 14, 0, 13 ] , [ 27, 0, 0, 27 ] , [ 27, 14, 14, 27 ]
  28F6 96 1 32 0 0 [ 1, 7, 7, 22 ] , [ 1, 14, 21, 15 ] , [ 13, 0, 0, 13 ] , [ 15, 0, 0, 15 ] , [ 17, 24, 8, 13 ]
  28G6 96 1 48 0 0 [ 1, 14, 21, 15 ] , [ 13, 0, 0, 13 ] , [ 13, 24, 16, 21 ] , [ 15, 0, 0, 15 ] , [ 17, 24, 8, 13 ]
  28H6 112 1 112 8 1 [ 1, 12, 8, 13 ] , [ 1, 26, 1, 27 ] , [ 9, 16, 0, 25 ] , [ 13, 0, 0, 13 ] , [ 15, 0, 0, 15 ] , [ 15, 7, 21, 8 ]
  28I6 126 1 63 10 0 [ 1, 0, 14, 1 ] , [ 1, 12, 8, 13 ] , [ 1, 14, 21, 15 ] , [ 5, 8, 16, 9 ] , [ 13, 0, 0, 13 ] , [ 15, 0, 14, 15 ] , [ 21, 16, 24, 21 ]
  28J6 126 2 63 4 0 [ 1, 0, 14, 1 ] , [ 1, 0, 21, 1 ] , [ 5, 8, 16, 9 ] , [ 13, 0, 0, 13 ] , [ 15, 0, 14, 15 ] , [ 15, 26, 22, 27 ] , [ 21, 16, 24, 21 ]
^ Level 30 Name Index  con   len   c2   c3  > SL(2,Z/30Z) Matrix Generators
  30A6 90 1 45 2 0 [ 1, 0, 15, 1 ] , [ 1, 18, 6, 19 ] , [ 1, 24, 18, 13 ] , [ 11, 0, 0, 11 ] , [ 13, 0, 18, 7 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 20, 21 ]
  30B6 90 1 45 4 0 [ 1, 18, 6, 19 ] , [ 1, 20, 20, 11 ] , [ 1, 24, 18, 13 ] , [ 11, 0, 0, 11 ] , [ 11, 20, 5, 1 ] , [ 13, 0, 18, 7 ] , [ 19, 0, 0, 19 ]
  30C6 108 1 18 0 0 [ 1, 10, 10, 11 ] , [ 1, 15, 0, 1 ] , [ 11, 0, 0, 11 ] , [ 21, 10, 20, 21 ] , [ 25, 12, 12, 7 ] , [ 29, 0, 0, 29 ]
  30D6 108 1 54 4 0 [ 1, 25, 10, 11 ] , [ 11, 0, 0, 11 ] , [ 21, 10, 20, 21 ] , [ 25, 12, 12, 7 ] , [ 27, 25, 2, 3 ] , [ 29, 0, 0, 29 ]
  30E6 120 1 40 0 6 [ 1, 20, 10, 21 ] , [ 7, 0, 24, 13 ] , [ 7, 18, 0, 13 ] , [ 19, 0, 0, 19 ] , [ 21, 20, 10, 11 ] , [ 28, 3, 9, 1 ]
  30F6 120 2 60 4 6 [ 13, 4, 10, 17 ] , [ 16, 15, 15, 1 ] , [ 17, 10, 22, 13 ] , [ 19, 0, 15, 19 ] , [ 19, 24, 16, 25 ] , [ 29, 0, 0, 29 ]
^ Level 31 Name Index  con   len   c2   c3  > SL(2,Z/31Z) Matrix Generators
  31A6 96 1 32 0 0 [ 0, 29, 16, 12 ] , [ 15, 19, 6, 18 ] , [ 16, 27, 2, 17 ] , [ 30, 0, 0, 30 ]
  31B6 160 1 32 0 10 [ 15, 19, 6, 18 ] , [ 16, 21, 18, 14 ] , [ 17, 3, 1, 13 ] , [ 30, 0, 0, 30 ]
^ Level 32 Name Index  con   len   c2   c3  > SL(2,Z/32Z) Matrix Generators
  32A6 96 1 12 0 0 [ 1, 4, 16, 1 ] , [ 1, 8, 0, 1 ] , [ 1, 16, 0, 1 ] , [ 9, 8, 16, 25 ] , [ 13, 16, 24, 5 ] , [ 15, 14, 8, 31 ] , [ 17, 4, 16, 17 ] , [ 17, 16, 0, 17 ] , [ 21, 2, 0, 29 ] , [ 29, 2, 16, 21 ]
  32B6 96 1 24 0 0 [ 1, 16, 16, 1 ] , [ 7, 28, 4, 7 ] , [ 8, 5, 19, 4 ] , [ 9, 16, 16, 25 ] , [ 9, 24, 8, 25 ] , [ 11, 28, 20, 19 ] , [ 16, 9, 7, 12 ] , [ 17, 0, 0, 17 ] , [ 21, 16, 0, 29 ] , [ 29, 4, 12, 5 ] , [ 31, 28, 4, 15 ]
  32C6 96 2 24 4 0 [ 3, 24, 16, 11 ] , [ 7, 8, 8, 23 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 17 ] , [ 17, 24, 8, 17 ] , [ 23, 20, 12, 23 ] , [ 25, 8, 8, 9 ] , [ 28, 1, 15, 12 ] , [ 29, 4, 4, 5 ] , [ 31, 8, 24, 31 ]
  32D6 96 2 24 4 0 [ 1, 12, 20, 17 ] , [ 3, 24, 0, 11 ] , [ 8, 7, 9, 8 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 17 ] , [ 17, 24, 8, 17 ] , [ 23, 20, 28, 23 ] , [ 25, 8, 8, 9 ] , [ 29, 4, 4, 5 ] , [ 31, 8, 24, 31 ]
  32E6 96 2 24 4 0 [ 1, 8, 24, 1 ] , [ 1, 16, 16, 1 ] , [ 13, 12, 12, 21 ] , [ 14, 27, 1, 2 ] , [ 17, 16, 16, 17 ] , [ 18, 7, 13, 30 ] , [ 25, 24, 24, 9 ] , [ 31, 0, 0, 31 ] , [ 31, 22, 14, 11 ] , [ 31, 24, 8, 31 ]
  32F6 96 2 24 4 0 [ 1, 8, 24, 1 ] , [ 1, 16, 16, 1 ] , [ 13, 12, 12, 21 ] , [ 14, 27, 1, 2 ] , [ 17, 16, 16, 17 ] , [ 20, 13, 11, 4 ] , [ 25, 24, 24, 9 ] , [ 31, 0, 0, 31 ] , [ 31, 22, 30, 11 ] , [ 31, 24, 8, 31 ]
  32G6 128 2 64 4 8 [ 8, 25, 23, 24 ] , [ 17, 0, 16, 17 ] , [ 17, 16, 0, 17 ] , [ 21, 21, 13, 10 ] , [ 25, 8, 16, 9 ] , [ 25, 16, 8, 9 ] , [ 31, 0, 0, 31 ]
  32H6 192 1 48 4 0 [ 0, 1, 31, 0 ] , [ 1, 16, 16, 1 ] , [ 5, 28, 4, 29 ] , [ 9, 0, 0, 25 ] , [ 9, 24, 8, 25 ] , [ 17, 0, 0, 17 ] , [ 20, 5, 3, 20 ] , [ 25, 0, 0, 9 ] , [ 31, 0, 0, 31 ] , [ 31, 8, 24, 31 ]
^ Level 35 Name Index  con   len   c2   c3  > SL(2,Z/35Z) Matrix Generators
  35A6 84 2 42 0 0 [ 1, 0, 14, 1 ] , [ 6, 0, 0, 6 ] , [ 11, 25, 0, 16 ] , [ 16, 30, 15, 26 ] , [ 21, 10, 30, 21 ] , [ 26, 20, 25, 26 ] , [ 34, 0, 0, 34 ]
  35B6 105 2 35 9 0 [ 1, 25, 10, 6 ] , [ 6, 0, 0, 6 ] , [ 6, 20, 15, 21 ] , [ 11, 20, 10, 31 ] , [ 15, 28, 28, 15 ] , [ 16, 30, 15, 26 ] , [ 22, 0, 0, 8 ] , [ 29, 0, 0, 29 ]
  35C6 120 1 40 0 6 [ 1, 0, 20, 1 ] , [ 4, 14, 31, 30 ] , [ 6, 0, 10, 6 ] , [ 22, 0, 14, 8 ] , [ 22, 28, 0, 8 ] , [ 29, 0, 0, 29 ]
  35D6 120 1 40 0 6 [ 1, 0, 20, 1 ] , [ 6, 0, 10, 6 ] , [ 9, 14, 11, 25 ] , [ 22, 0, 14, 8 ] , [ 22, 28, 0, 8 ] , [ 29, 0, 0, 29 ]
  35E6 126 1 126 10 0 [ 1, 0, 14, 1 ] , [ 6, 0, 0, 6 ] , [ 16, 30, 15, 26 ] , [ 21, 10, 30, 21 ] , [ 26, 20, 25, 26 ] , [ 33, 30, 29, 2 ] , [ 34, 0, 0, 34 ]
^ Level 36 Name Index  con   len   c2   c3  > SL(2,Z/36Z) Matrix Generators
  36A6 72 1 36 0 0 [ 1, 4, 28, 5 ] , [ 1, 24, 12, 1 ] , [ 10, 27, 27, 1 ] , [ 13, 0, 24, 25 ] , [ 19, 0, 0, 19 ] , [ 29, 12, 12, 5 ] , [ 29, 28, 4, 25 ]
  36B6 96 1 32 0 3 [ 13, 0, 0, 25 ] , [ 19, 0, 0, 19 ] , [ 25, 0, 24, 13 ] , [ 28, 15, 33, 19 ] , [ 28, 27, 25, 19 ] , [ 35, 0, 0, 35 ]
  36C6 108 1 27 8 0 [ 1, 0, 18, 1 ] , [ 13, 0, 24, 25 ] , [ 19, 0, 18, 19 ] , [ 23, 0, 30, 11 ] , [ 25, 12, 0, 13 ] , [ 29, 28, 22, 25 ] , [ 33, 10, 17, 15 ]
  36D6 108 1 54 0 0 [ 1, 0, 18, 1 ] , [ 1, 12, 0, 1 ] , [ 13, 0, 12, 25 ] , [ 17, 0, 18, 17 ] , [ 19, 0, 18, 19 ] , [ 29, 2, 26, 13 ] , [ 29, 32, 17, 25 ]
  36E6 108 1 54 10 0 [ 15, 32, 34, 27 ] , [ 19, 0, 0, 19 ] , [ 19, 28, 10, 11 ] , [ 25, 12, 0, 13 ] , [ 25, 24, 24, 13 ] , [ 29, 0, 24, 5 ] , [ 33, 10, 35, 15 ]
  36F6 108 1 54 10 0 [ 1, 4, 28, 5 ] , [ 1, 24, 12, 1 ] , [ 13, 0, 24, 25 ] , [ 19, 0, 0, 19 ] , [ 28, 9, 27, 28 ] , [ 29, 12, 12, 5 ] , [ 29, 28, 4, 25 ]
  36G6 108 1 108 6 3 [ 1, 12, 20, 25 ] , [ 1, 27, 27, 10 ] , [ 1, 32, 32, 17 ] , [ 4, 1, 19, 32 ] , [ 5, 8, 8, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 0, 19 ]
  36H6 108 2 27 4 0 [ 1, 0, 18, 1 ] , [ 11, 14, 32, 31 ] , [ 13, 0, 15, 25 ] , [ 19, 0, 18, 19 ] , [ 23, 0, 30, 11 ] , [ 25, 0, 12, 13 ] , [ 25, 12, 0, 13 ]
  36I6 108 2 54 10 0 [ 15, 32, 34, 27 ] , [ 19, 0, 0, 19 ] , [ 23, 34, 13, 13 ] , [ 25, 12, 0, 13 ] , [ 25, 24, 24, 13 ] , [ 29, 0, 24, 5 ] , [ 33, 10, 35, 15 ]
  36J6 144 1 12 0 12 [ 1, 0, 12, 1 ] , [ 1, 9, 9, 10 ] , [ 1, 18, 18, 1 ] , [ 19, 0, 18, 19 ] , [ 25, 24, 16, 1 ] , [ 35, 0, 0, 35 ]
  36K6 144 1 24 0 12 [ 1, 0, 24, 1 ] , [ 1, 6, 34, 25 ] , [ 1, 18, 18, 1 ] , [ 19, 0, 30, 19 ] , [ 19, 3, 29, 16 ] , [ 19, 18, 0, 19 ] , [ 35, 0, 0, 35 ]
^ Level 39 Name Index  con   len   c2   c3  > SL(2,Z/39Z) Matrix Generators
  39A6 84 1 14 0 0 [ 7, 6, 36, 31 ] , [ 10, 12, 3, 31 ] , [ 14, 0, 0, 14 ] , [ 14, 26, 26, 1 ] , [ 27, 13, 26, 27 ] , [ 38, 0, 0, 38 ]
^ Level 42 Name Index  con   len   c2   c3  > SL(2,Z/42Z) Matrix Generators
  42A6 84 2 21 4 0 [ 1, 28, 7, 29 ] , [ 7, 12, 18, 7 ] , [ 13, 0, 0, 13 ] , [ 19, 36, 30, 37 ] , [ 22, 21, 21, 1 ] , [ 25, 12, 0, 37 ] , [ 29, 0, 0, 29 ] , [ 41, 8, 2, 25 ]
  42B6 84 2 28 0 3 [ 1, 28, 28, 29 ] , [ 7, 12, 18, 7 ] , [ 13, 0, 0, 13 ] , [ 22, 35, 21, 1 ] , [ 25, 18, 36, 31 ] , [ 29, 0, 0, 29 ] , [ 29, 28, 28, 1 ] , [ 41, 39, 33, 14 ]
  42C6 84 2 84 0 0 [ 1, 14, 0, 1 ] , [ 1, 21, 0, 1 ] , [ 1, 24, 30, 7 ] , [ 1, 30, 18, 37 ] , [ 7, 12, 18, 7 ] , [ 13, 0, 0, 13 ] , [ 29, 21, 0, 29 ] , [ 37, 6, 12, 19 ]
  42D6 126 2 63 16 0 [ 1, 21, 21, 22 ] , [ 13, 0, 0, 13 ] , [ 13, 24, 18, 1 ] , [ 15, 2, 4, 9 ] , [ 15, 14, 7, 15 ] , [ 19, 36, 30, 37 ] , [ 29, 0, 0, 29 ] , [ 29, 28, 7, 1 ]
^ Level 44 Name Index  con   len   c2   c3  > SL(2,Z/44Z) Matrix Generators
  44A6 88 2 44 0 4 [ 22, 3, 7, 33 ] , [ 22, 13, 5, 43 ] , [ 23, 0, 0, 23 ] , [ 34, 11, 11, 1 ] , [ 43, 0, 0, 43 ]
^ Level 45 Name Index  con   len   c2   c3  > SL(2,Z/45Z) Matrix Generators
  45A6 90 1 15 6 0 [ 1, 15, 30, 1 ] , [ 11, 0, 30, 41 ] , [ 16, 0, 15, 31 ] , [ 19, 0, 0, 19 ] , [ 22, 18, 21, 7 ] , [ 26, 20, 35, 1 ] , [ 28, 0, 18, 37 ] , [ 37, 36, 0, 28 ]
  45B6 90 1 30 6 0 [ 1, 30, 15, 1 ] , [ 2, 3, 21, 32 ] , [ 2, 32, 14, 22 ] , [ 19, 0, 0, 19 ] , [ 22, 18, 36, 7 ] , [ 28, 0, 18, 37 ] , [ 31, 0, 30, 16 ] , [ 37, 36, 0, 28 ]
  45C6 90 1 90 2 0 [ 11, 5, 5, 31 ] , [ 11, 30, 30, 41 ] , [ 19, 0, 0, 19 ] , [ 28, 0, 18, 37 ] , [ 31, 0, 30, 16 ] , [ 31, 15, 30, 16 ] , [ 37, 18, 36, 37 ] , [ 37, 36, 0, 28 ]
  45D6 108 1 54 8 0 [ 1, 40, 40, 26 ] , [ 16, 0, 15, 31 ] , [ 19, 36, 36, 28 ] , [ 24, 2, 4, 36 ] , [ 28, 9, 9, 19 ] , [ 31, 15, 15, 16 ] , [ 41, 0, 15, 11 ] , [ 44, 30, 15, 44 ]
^ Level 48 Name Index  con   len   c2   c3  > SL(2,Z/48Z) Matrix Generators
  48A6 72 1 3 0 0 [ 1, 0, 24, 1 ] , [ 17, 0, 0, 17 ] , [ 17, 32, 32, 1 ] , [ 23, 0, 24, 23 ] , [ 25, 0, 24, 25 ] , [ 25, 20, 14, 17 ] , [ 33, 32, 16, 33 ] , [ 37, 0, 36, 13 ] , [ 39, 34, 35, 33 ] , [ 41, 24, 36, 41 ]
  48B6 72 1 12 0 0 [ 1, 0, 24, 1 ] , [ 1, 32, 32, 17 ] , [ 15, 44, 22, 39 ] , [ 17, 0, 0, 17 ] , [ 17, 32, 32, 1 ] , [ 25, 0, 24, 25 ] , [ 31, 34, 1, 29 ] , [ 35, 24, 12, 11 ] , [ 37, 0, 0, 13 ] , [ 41, 24, 36, 41 ]
  48C6 72 1 36 0 0 [ 1, 0, 24, 1 ] , [ 15, 44, 22, 39 ] , [ 17, 0, 0, 17 ] , [ 25, 0, 24, 25 ] , [ 31, 34, 1, 29 ] , [ 35, 24, 12, 11 ] , [ 37, 0, 0, 13 ] , [ 41, 24, 36, 41 ] , [ 47, 4, 22, 7 ] , [ 47, 20, 38, 7 ]
  48D6 96 1 48 0 0 [ 1, 0, 32, 1 ] , [ 1, 24, 24, 1 ] , [ 4, 27, 45, 4 ] , [ 7, 36, 12, 7 ] , [ 13, 36, 12, 37 ] , [ 17, 0, 16, 17 ] , [ 22, 39, 21, 46 ] , [ 25, 0, 0, 25 ] , [ 37, 24, 24, 13 ]
  48E6 96 1 48 8 0 [ 0, 17, 31, 36 ] , [ 1, 24, 24, 1 ] , [ 13, 36, 24, 37 ] , [ 13, 45, 45, 34 ] , [ 17, 0, 24, 17 ] , [ 17, 16, 4, 1 ] , [ 25, 24, 0, 25 ] , [ 25, 36, 36, 25 ] , [ 47, 36, 12, 47 ]
  48F6 96 1 48 8 0 [ 0, 17, 31, 36 ] , [ 1, 16, 4, 17 ] , [ 1, 24, 24, 1 ] , [ 13, 36, 24, 37 ] , [ 13, 45, 45, 34 ] , [ 17, 0, 24, 17 ] , [ 25, 24, 0, 25 ] , [ 25, 36, 36, 25 ] , [ 47, 36, 12, 47 ]
  48G6 96 2 24 8 0 [ 0, 1, 47, 24 ] , [ 1, 24, 24, 1 ] , [ 1, 32, 8, 17 ] , [ 13, 21, 21, 34 ] , [ 13, 36, 24, 37 ] , [ 17, 0, 0, 17 ] , [ 25, 24, 0, 25 ] , [ 25, 36, 36, 25 ] , [ 47, 24, 24, 47 ]
  48H6 96 2 24 8 0 [ 0, 1, 47, 0 ] , [ 1, 16, 16, 17 ] , [ 13, 24, 36, 37 ] , [ 17, 0, 0, 17 ] , [ 25, 0, 24, 25 ] , [ 25, 24, 0, 25 ] , [ 34, 3, 3, 13 ] , [ 37, 36, 0, 13 ] , [ 47, 0, 0, 47 ]
  48I6 144 1 36 8 0 [ 1, 0, 18, 1 ] , [ 1, 0, 24, 1 ] , [ 5, 24, 24, 29 ] , [ 17, 0, 0, 17 ] , [ 17, 0, 36, 17 ] , [ 23, 14, 11, 13 ] , [ 25, 0, 0, 25 ] , [ 25, 0, 24, 25 ] , [ 35, 24, 36, 11 ] , [ 47, 22, 19, 13 ]
  48J6 144 1 36 8 0 [ 1, 0, 18, 1 ] , [ 1, 0, 24, 1 ] , [ 5, 24, 24, 29 ] , [ 17, 0, 0, 17 ] , [ 17, 0, 36, 17 ] , [ 23, 14, 11, 13 ] , [ 25, 0, 0, 25 ] , [ 25, 0, 24, 25 ] , [ 33, 16, 32, 33 ] , [ 35, 24, 36, 11 ]
  48K6 144 1 72 8 0 [ 1, 0, 12, 1 ] , [ 1, 0, 24, 1 ] , [ 5, 0, 12, 29 ] , [ 23, 34, 1, 37 ] , [ 23, 34, 7, 25 ] , [ 25, 0, 0, 25 ] , [ 25, 0, 24, 25 ] , [ 37, 24, 24, 13 ] , [ 43, 46, 19, 17 ] , [ 47, 0, 0, 47 ]
^ Level 50 Name Index  con   len   c2   c3  > SL(2,Z/50Z) Matrix Generators
  50A6 90 1 90 2 0 [ 1, 0, 25, 1 ] , [ 11, 30, 30, 41 ] , [ 21, 20, 0, 31 ] , [ 29, 30, 0, 19 ] , [ 33, 8, 30, 27 ] , [ 43, 26, 26, 39 ]
  50B6 90 1 90 2 0 [ 1, 0, 25, 1 ] , [ 7, 48, 8, 5 ] , [ 19, 6, 38, 41 ] , [ 31, 0, 30, 21 ] , [ 31, 40, 40, 21 ] , [ 41, 16, 6, 17 ]
  50C6 90 1 90 2 0 [ 1, 0, 25, 1 ] , [ 9, 4, 44, 3 ] , [ 9, 20, 40, 39 ] , [ 19, 38, 21, 21 ] , [ 31, 30, 0, 21 ] , [ 41, 20, 20, 11 ]
  50D6 90 1 90 2 0 [ 1, 0, 25, 1 ] , [ 29, 0, 30, 19 ] , [ 37, 30, 42, 3 ] , [ 41, 0, 40, 11 ] , [ 41, 20, 20, 11 ] , [ 49, 14, 34, 23 ]
  50E6 180 1 90 4 0 [ 5, 32, 12, 47 ] , [ 19, 26, 33, 11 ] , [ 19, 40, 30, 29 ] , [ 21, 10, 10, 31 ] , [ 21, 20, 0, 31 ]
^ Level 52 Name Index  con   len   c2   c3  > SL(2,Z/52Z) Matrix Generators
  52A6 84 1 42 0 0 [ 1, 0, 26, 1 ] , [ 1, 32, 32, 37 ] , [ 25, 0, 0, 25 ] , [ 27, 0, 26, 27 ] , [ 29, 6, 20, 49 ] , [ 29, 32, 33, 49 ] , [ 45, 24, 32, 9 ]
^ Level 54 Name Index  con   len   c2   c3  > SL(2,Z/54Z) Matrix Generators
  54A6 72 1 12 0 0 [ 1, 0, 18, 1 ] , [ 25, 24, 22, 19 ] , [ 28, 27, 27, 1 ] , [ 31, 0, 30, 7 ] , [ 37, 0, 18, 19 ] , [ 37, 0, 36, 19 ] , [ 37, 18, 24, 19 ] , [ 53, 0, 0, 53 ]
  54B6 108 1 36 0 0 [ 1, 0, 18, 1 ] , [ 1, 0, 27, 1 ] , [ 1, 0, 42, 1 ] , [ 17, 0, 0, 35 ] , [ 31, 0, 0, 7 ] , [ 37, 0, 0, 19 ] , [ 37, 0, 42, 19 ] , [ 49, 36, 22, 25 ]
^ Level 56 Name Index  con   len   c2   c3  > SL(2,Z/56Z) Matrix Generators
  56A6 84 2 21 4 0 [ 1, 7, 42, 15 ] , [ 1, 16, 4, 9 ] , [ 1, 28, 0, 1 ] , [ 15, 0, 0, 15 ] , [ 15, 42, 28, 15 ] , [ 29, 28, 0, 29 ] , [ 33, 8, 16, 9 ] , [ 41, 0, 0, 41 ] , [ 49, 8, 48, 41 ] , [ 49, 40, 32, 49 ]
  56B6 84 2 42 0 0 [ 1, 7, 0, 1 ] , [ 1, 14, 0, 1 ] , [ 1, 28, 0, 1 ] , [ 9, 48, 40, 33 ] , [ 15, 42, 0, 15 ] , [ 23, 26, 52, 15 ] , [ 29, 28, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 49, 8, 48, 41 ] , [ 49, 16, 24, 49 ]
  56C6 84 2 42 0 0 [ 1, 7, 0, 1 ] , [ 1, 14, 0, 1 ] , [ 1, 28, 0, 1 ] , [ 9, 40, 24, 1 ] , [ 9, 48, 40, 33 ] , [ 15, 42, 0, 15 ] , [ 29, 28, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 49, 8, 48, 41 ] , [ 49, 16, 24, 49 ]
  56D6 96 1 24 0 0 [ 1, 0, 28, 1 ] , [ 11, 44, 39, 39 ] , [ 17, 0, 41, 33 ] , [ 25, 8, 40, 33 ] , [ 29, 0, 14, 29 ] , [ 29, 0, 28, 29 ] , [ 33, 8, 32, 1 ] , [ 33, 8, 46, 1 ] , [ 53, 44, 32, 53 ]
  56E6 96 1 48 0 0 [ 1, 0, 28, 1 ] , [ 15, 0, 0, 15 ] , [ 15, 42, 21, 29 ] , [ 17, 40, 10, 17 ] , [ 17, 40, 24, 17 ] , [ 29, 0, 0, 29 ] , [ 29, 0, 28, 29 ] , [ 41, 40, 40, 9 ] , [ 49, 16, 24, 9 ]
  56F6 112 2 28 8 4 [ 1, 28, 28, 1 ] , [ 9, 48, 40, 33 ] , [ 23, 47, 38, 29 ] , [ 29, 0, 28, 29 ] , [ 29, 35, 35, 50 ] , [ 41, 0, 0, 41 ] , [ 41, 48, 8, 49 ] , [ 43, 28, 0, 43 ] , [ 49, 16, 24, 49 ]
  56G6 112 2 28 8 4 [ 1, 28, 28, 1 ] , [ 9, 48, 40, 33 ] , [ 15, 39, 10, 41 ] , [ 22, 49, 21, 1 ] , [ 29, 28, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 41, 48, 8, 49 ] , [ 47, 8, 16, 23 ] , [ 49, 16, 24, 49 ]
  56H6 112 2 112 12 1 [ 9, 40, 24, 1 ] , [ 9, 48, 40, 33 ] , [ 15, 0, 0, 15 ] , [ 15, 7, 42, 1 ] , [ 22, 49, 21, 1 ] , [ 29, 0, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 49, 24, 16, 41 ] , [ 49, 40, 32, 49 ]
^ Level 58 Name Index  con   len   c2   c3  > SL(2,Z/58Z) Matrix Generators
  58A6 Γ0(58) 90 1 90 2 0 [ 1, 0, 29, 1 ] , [ 25, 30, 30, 43 ] , [ 51, 0, 48, 33 ] , [ 51, 50, 16, 43 ] , [ 55, 16, 28, 5 ]
^ Level 60 Name Index  con   len   c2   c3  > SL(2,Z/60Z) Matrix Generators
  60A6 80 1 80 0 2 [ 1, 0, 20, 1 ] , [ 1, 36, 48, 49 ] , [ 11, 48, 4, 23 ] , [ 16, 45, 15, 16 ] , [ 29, 0, 0, 29 ] , [ 31, 0, 0, 31 ] , [ 37, 0, 56, 13 ] , [ 41, 0, 40, 41 ] , [ 46, 15, 15, 1 ]
  60B6 90 1 15 6 0 [ 1, 0, 30, 1 ] , [ 1, 20, 20, 41 ] , [ 1, 24, 48, 13 ] , [ 1, 48, 36, 49 ] , [ 13, 0, 48, 37 ] , [ 31, 0, 30, 31 ] , [ 31, 30, 15, 1 ] , [ 41, 0, 0, 41 ] , [ 41, 20, 20, 1 ] , [ 49, 0, 0, 49 ]
  60C6 90 1 45 4 0 [ 1, 0, 15, 1 ] , [ 1, 0, 30, 1 ] , [ 1, 20, 20, 41 ] , [ 1, 24, 48, 13 ] , [ 1, 48, 36, 49 ] , [ 13, 0, 48, 37 ] , [ 31, 0, 30, 31 ] , [ 41, 0, 0, 41 ] , [ 41, 50, 20, 1 ] , [ 49, 0, 0, 49 ]
  60D6 90 2 15 6 0 [ 1, 0, 30, 1 ] , [ 1, 24, 8, 13 ] , [ 1, 40, 40, 41 ] , [ 21, 40, 20, 21 ] , [ 31, 0, 30, 31 ] , [ 31, 30, 45, 1 ] , [ 37, 0, 12, 13 ] , [ 41, 0, 0, 41 ] , [ 49, 0, 0, 49 ] , [ 49, 12, 24, 1 ]
  60E6 108 1 54 4 0 [ 21, 40, 20, 21 ] , [ 25, 12, 12, 37 ] , [ 27, 10, 2, 3 ] , [ 29, 0, 0, 29 ] , [ 31, 0, 0, 31 ] , [ 31, 15, 0, 31 ] , [ 31, 30, 0, 31 ] , [ 31, 55, 10, 41 ] , [ 41, 0, 0, 41 ]
  60F6 108 1 54 8 0 [ 1, 40, 40, 41 ] , [ 25, 12, 12, 37 ] , [ 27, 10, 32, 3 ] , [ 29, 0, 0, 29 ] , [ 31, 0, 0, 31 ] , [ 31, 15, 30, 1 ] , [ 31, 30, 0, 31 ] , [ 41, 0, 0, 41 ] , [ 47, 30, 42, 23 ]
^ Level 63 Name Index  con   len   c2   c3  > SL(2,Z/63Z) Matrix Generators
  63A6 72 1 72 0 0 [ 1, 0, 18, 1 ] , [ 1, 14, 14, 8 ] , [ 1, 14, 59, 8 ] , [ 8, 0, 0, 8 ] , [ 13, 0, 42, 34 ] , [ 16, 0, 21, 4 ] , [ 22, 0, 42, 43 ] , [ 22, 42, 0, 43 ] , [ 43, 0, 21, 22 ] , [ 57, 56, 49, 15 ]
  63B6 84 2 28 0 0 [ 1, 18, 45, 55 ] , [ 1, 42, 42, 1 ] , [ 15, 14, 28, 1 ] , [ 15, 46, 38, 41 ] , [ 28, 18, 54, 28 ] , [ 43, 0, 21, 22 ] , [ 43, 49, 56, 36 ] , [ 46, 27, 45, 10 ] , [ 50, 35, 7, 15 ] , [ 55, 0, 0, 55 ] , [ 55, 27, 36, 28 ]
  63C6 84 2 28 0 3 [ 1, 18, 45, 55 ] , [ 1, 28, 35, 36 ] , [ 1, 42, 42, 1 ] , [ 15, 4, 59, 20 ] , [ 15, 56, 7, 22 ] , [ 28, 18, 54, 28 ] , [ 29, 14, 49, 15 ] , [ 43, 0, 21, 22 ] , [ 46, 27, 45, 10 ] , [ 55, 0, 0, 55 ] , [ 55, 27, 36, 28 ]
  63D6 96 2 32 0 3 [ 1, 0, 9, 1 ] , [ 1, 0, 21, 1 ] , [ 4, 42, 36, 16 ] , [ 8, 0, 0, 8 ] , [ 13, 42, 14, 55 ] , [ 25, 0, 22, 58 ] , [ 29, 21, 49, 29 ] , [ 34, 0, 0, 13 ] , [ 43, 0, 0, 22 ] , [ 43, 0, 21, 22 ]
  63E6 126 2 21 18 0 [ 1, 42, 21, 1 ] , [ 10, 36, 18, 46 ] , [ 19, 36, 45, 19 ] , [ 19, 54, 27, 37 ] , [ 22, 0, 21, 43 ] , [ 28, 18, 54, 28 ] , [ 43, 0, 42, 22 ] , [ 46, 27, 45, 10 ] , [ 50, 0, 42, 29 ] , [ 55, 0, 0, 55 ] , [ 55, 27, 36, 28 ] , [ 62, 62, 29, 28 ]
  63F6 126 2 63 18 0 [ 1, 42, 21, 1 ] , [ 10, 36, 18, 46 ] , [ 17, 44, 2, 46 ] , [ 19, 54, 27, 37 ] , [ 22, 0, 21, 43 ] , [ 28, 18, 54, 28 ] , [ 43, 0, 42, 22 ] , [ 46, 27, 45, 10 ] , [ 49, 29, 20, 62 ] , [ 50, 0, 42, 29 ] , [ 55, 0, 0, 55 ] , [ 55, 27, 36, 28 ]
  63G6 126 2 63 18 0 [ 1, 42, 21, 1 ] , [ 10, 36, 18, 46 ] , [ 17, 44, 2, 46 ] , [ 19, 54, 27, 37 ] , [ 22, 0, 21, 43 ] , [ 28, 18, 54, 28 ] , [ 36, 7, 14, 15 ] , [ 43, 0, 42, 22 ] , [ 46, 27, 45, 10 ] , [ 50, 0, 42, 29 ] , [ 55, 0, 0, 55 ] , [ 55, 27, 36, 28 ]
^ Level 64 Name Index  con   len   c2   c3  > SL(2,Z/64Z) Matrix Generators
  64A6 96 1 24 0 0 [ 1, 32, 32, 1 ] , [ 3, 4, 60, 59 ] , [ 13, 12, 52, 53 ] , [ 15, 30, 34, 51 ] , [ 25, 8, 24, 41 ] , [ 25, 16, 0, 41 ] , [ 25, 24, 40, 41 ] , [ 33, 32, 32, 33 ] , [ 37, 52, 44, 29 ] , [ 39, 38, 58, 27 ] , [ 41, 24, 8, 25 ] , [ 43, 38, 50, 7 ] , [ 44, 53, 27, 34 ] , [ 49, 16, 48, 17 ]
^ Level 66 Name Index  con   len   c2   c3  > SL(2,Z/66Z) Matrix Generators
  66A6 66 2 11 0 0 [ 1, 22, 22, 23 ] , [ 1, 44, 44, 23 ] , [ 11, 26, 8, 7 ] , [ 23, 0, 0, 23 ] , [ 23, 55, 55, 34 ] , [ 26, 7, 7, 7 ] , [ 34, 33, 33, 1 ] , [ 65, 0, 0, 65 ]
  66B6 72 1 12 0 0 [ 1, 22, 22, 23 ] , [ 1, 33, 33, 34 ] , [ 23, 0, 0, 23 ] , [ 34, 33, 33, 1 ] , [ 43, 33, 33, 10 ] , [ 43, 44, 44, 65 ] , [ 45, 22, 44, 45 ] , [ 46, 3, 51, 55 ] , [ 56, 9, 27, 35 ] , [ 61, 48, 24, 7 ]
  66C6 72 1 24 0 0 [ 1, 22, 22, 23 ] , [ 1, 33, 55, 34 ] , [ 13, 36, 18, 55 ] , [ 13, 42, 54, 7 ] , [ 23, 0, 0, 23 ] , [ 31, 24, 12, 37 ] , [ 45, 44, 22, 45 ] , [ 49, 36, 36, 13 ]
  66D6 72 1 36 0 0 [ 1, 22, 55, 23 ] , [ 1, 33, 33, 34 ] , [ 23, 0, 0, 23 ] , [ 34, 33, 33, 1 ] , [ 43, 44, 11, 65 ] , [ 45, 22, 44, 45 ] , [ 46, 3, 51, 55 ] , [ 56, 9, 27, 35 ] , [ 56, 55, 55, 34 ] , [ 61, 48, 24, 7 ]
  66E6 88 2 44 0 4 [ 1, 0, 22, 1 ] , [ 1, 0, 44, 1 ] , [ 10, 21, 39, 49 ] , [ 23, 0, 22, 23 ] , [ 34, 33, 33, 1 ] , [ 35, 24, 36, 53 ] , [ 43, 0, 0, 43 ]
  66F6 99 2 33 9 0 [ 1, 22, 22, 23 ] , [ 1, 33, 0, 1 ] , [ 1, 44, 44, 23 ] , [ 11, 59, 8, 7 ] , [ 23, 0, 0, 23 ] , [ 23, 55, 22, 1 ] , [ 59, 7, 40, 7 ] , [ 65, 0, 0, 65 ]
^ Level 69 Name Index  con   len   c2   c3  > SL(2,Z/69Z) Matrix Generators
  69A6 72 1 24 0 0 [ 24, 23, 46, 24 ] , [ 28, 60, 51, 28 ] , [ 45, 23, 46, 45 ] , [ 47, 0, 0, 47 ] , [ 47, 23, 23, 1 ] , [ 67, 27, 15, 4 ]
^ Level 70 Name Index  con   len   c2   c3  > SL(2,Z/70Z) Matrix Generators
  70A6 84 2 42 4 0 [ 1, 35, 35, 36 ] , [ 11, 10, 0, 51 ] , [ 11, 50, 60, 31 ] , [ 15, 28, 28, 57 ] , [ 23, 57, 45, 2 ] , [ 29, 0, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 43, 42, 35, 57 ] , [ 61, 30, 50, 51 ]
^ Level 71 Name Index  con   len   c2   c3  > SL(2,Z/71Z) Matrix Generators
  71A6 Γ0(71) 72 1 72 0 0 [ 6, 17, 18, 63 ] , [ 50, 70, 61, 13 ] , [ 68, 42, 65, 60 ] , [ 70, 0, 0, 70 ]
^ Level 72 Name Index  con   len   c2   c3  > SL(2,Z/72Z) Matrix Generators
  72A6 96 2 16 0 6 [ 1, 24, 0, 1 ] , [ 1, 36, 36, 1 ] , [ 10, 27, 27, 37 ] , [ 19, 0, 36, 19 ] , [ 25, 0, 0, 49 ] , [ 37, 0, 36, 37 ] , [ 37, 18, 27, 19 ] , [ 43, 42, 9, 49 ] , [ 46, 63, 27, 1 ] , [ 49, 8, 48, 49 ] , [ 55, 54, 45, 1 ] , [ 65, 8, 48, 17 ]
  72B6 108 1 27 12 0 [ 1, 18, 36, 1 ] , [ 1, 36, 0, 1 ] , [ 5, 60, 0, 29 ] , [ 17, 56, 8, 1 ] , [ 19, 9, 54, 37 ] , [ 19, 36, 0, 19 ] , [ 25, 48, 48, 49 ] , [ 33, 2, 40, 33 ] , [ 33, 56, 4, 33 ] , [ 37, 0, 0, 37 ] , [ 41, 24, 0, 65 ] , [ 49, 0, 48, 25 ] , [ 49, 48, 0, 25 ]
  72C6 108 1 54 10 0 [ 1, 18, 0, 1 ] , [ 1, 36, 0, 1 ] , [ 5, 42, 0, 29 ] , [ 17, 56, 8, 1 ] , [ 19, 9, 54, 37 ] , [ 19, 36, 0, 19 ] , [ 25, 48, 48, 49 ] , [ 33, 56, 40, 33 ] , [ 37, 0, 0, 37 ] , [ 41, 24, 0, 65 ] , [ 49, 0, 48, 25 ] , [ 49, 48, 0, 25 ]
  72D6 108 1 54 10 0 [ 1, 18, 0, 1 ] , [ 1, 36, 0, 1 ] , [ 5, 42, 0, 29 ] , [ 17, 56, 8, 1 ] , [ 19, 36, 0, 19 ] , [ 25, 48, 48, 49 ] , [ 33, 56, 4, 33 ] , [ 37, 0, 0, 37 ] , [ 41, 24, 0, 65 ] , [ 49, 0, 48, 25 ] , [ 49, 48, 0, 25 ] , [ 51, 65, 22, 69 ]
  72E6 108 2 54 10 0 [ 1, 18, 0, 1 ] , [ 1, 32, 8, 41 ] , [ 1, 36, 0, 1 ] , [ 5, 42, 0, 29 ] , [ 17, 56, 44, 1 ] , [ 19, 9, 54, 37 ] , [ 19, 36, 0, 19 ] , [ 25, 48, 48, 49 ] , [ 37, 0, 0, 37 ] , [ 41, 24, 0, 65 ] , [ 49, 0, 48, 25 ] , [ 49, 48, 0, 25 ]
^ Level 75 Name Index  con   len   c2   c3  > SL(2,Z/75Z) Matrix Generators
  75A6 90 1 30 6 0 [ 26, 0, 0, 26 ] , [ 26, 50, 50, 1 ] , [ 29, 5, 50, 19 ] , [ 43, 51, 51, 64 ] , [ 46, 45, 0, 31 ] , [ 51, 25, 50, 51 ] , [ 58, 8, 5, 2 ] , [ 61, 30, 30, 16 ]
  75B6 90 1 30 6 0 [ 1, 50, 50, 26 ] , [ 7, 48, 33, 55 ] , [ 16, 66, 6, 67 ] , [ 19, 6, 63, 16 ] , [ 26, 0, 0, 26 ] , [ 31, 0, 30, 46 ] , [ 31, 15, 15, 46 ] , [ 51, 50, 25, 51 ]
  75C6 90 1 30 6 0 [ 1, 25, 25, 26 ] , [ 1, 50, 50, 26 ] , [ 16, 45, 45, 61 ] , [ 19, 63, 21, 46 ] , [ 26, 0, 0, 26 ] , [ 31, 30, 0, 46 ] , [ 34, 45, 15, 64 ] , [ 34, 54, 69, 28 ] , [ 51, 50, 25, 51 ]
  75D6 90 1 30 6 0 [ 4, 0, 30, 19 ] , [ 16, 0, 15, 61 ] , [ 16, 45, 45, 61 ] , [ 26, 0, 0, 26 ] , [ 26, 50, 50, 1 ] , [ 37, 30, 42, 28 ] , [ 49, 39, 9, 73 ] , [ 51, 50, 25, 51 ]
^ Level 76 Name Index  con   len   c2   c3  > SL(2,Z/76Z) Matrix Generators
  76A6 80 1 80 0 2 [ 1, 38, 19, 39 ] , [ 21, 48, 36, 57 ] , [ 29, 12, 64, 37 ] , [ 39, 0, 0, 39 ] , [ 58, 19, 19, 1 ] , [ 69, 48, 28, 25 ] , [ 75, 0, 0, 75 ]
^ Level 77 Name Index  con   len   c2   c3  > SL(2,Z/77Z) Matrix Generators
  77A6 88 2 88 0 4 [ 1, 66, 22, 67 ] , [ 24, 48, 2, 65 ] , [ 34, 0, 0, 34 ] , [ 34, 55, 22, 56 ] , [ 36, 42, 49, 8 ] , [ 43, 0, 0, 43 ]
^ Level 78 Name Index  con   len   c2   c3  > SL(2,Z/78Z) Matrix Generators
  78A6 84 1 42 4 0 [ 7, 6, 36, 31 ] , [ 27, 52, 65, 27 ] , [ 40, 39, 39, 1 ] , [ 49, 12, 42, 31 ] , [ 53, 0, 0, 53 ] , [ 53, 26, 26, 1 ] , [ 69, 16, 68, 9 ] , [ 77, 0, 0, 77 ]
  78B6 84 2 28 0 3 [ 1, 52, 52, 53 ] , [ 13, 42, 30, 67 ] , [ 16, 57, 65, 61 ] , [ 25, 0, 0, 25 ] , [ 27, 26, 52, 27 ] , [ 53, 0, 0, 53 ] , [ 55, 6, 72, 49 ] , [ 61, 60, 26, 55 ]
^ Level 79 Name Index  con   len   c2   c3  > SL(2,Z/79Z) Matrix Generators
  79A6 Γ0(79) 80 1 80 0 2 [ 12, 42, 34, 73 ] , [ 13, 75, 11, 21 ] , [ 37, 63, 51, 10 ] , [ 78, 0, 0, 78 ]
^ Level 84 Name Index  con   len   c2   c3  > SL(2,Z/84Z) Matrix Generators
  84A6 96 2 16 0 6 [ 1, 42, 42, 1 ] , [ 1, 63, 35, 22 ] , [ 25, 36, 12, 61 ] , [ 29, 0, 0, 29 ] , [ 37, 40, 4, 77 ] , [ 43, 42, 0, 43 ] , [ 49, 36, 76, 13 ] , [ 57, 56, 28, 57 ] , [ 69, 68, 82, 37 ]
  84B6 126 2 21 18 0 [ 1, 28, 28, 29 ] , [ 13, 0, 0, 13 ] , [ 25, 60, 36, 73 ] , [ 29, 0, 0, 29 ] , [ 29, 0, 42, 29 ] , [ 37, 72, 0, 25 ] , [ 43, 0, 42, 43 ] , [ 49, 12, 60, 49 ] , [ 57, 28, 56, 57 ] , [ 61, 72, 60, 13 ] , [ 71, 14, 35, 1 ]
^ Level 86 Name Index  con   len   c2   c3  > SL(2,Z/86Z) Matrix Generators
  86A6 88 1 44 0 4 [ 1, 43, 43, 44 ] , [ 11, 36, 30, 67 ] , [ 17, 12, 66, 77 ] , [ 39, 26, 4, 49 ] , [ 67, 74, 40, 75 ]
^ Level 87 Name Index  con   len   c2   c3  > SL(2,Z/87Z) Matrix Generators
  87A6 90 1 30 6 0 [ 22, 0, 48, 4 ] , [ 22, 21, 45, 43 ] , [ 25, 30, 30, 43 ] , [ 55, 45, 57, 34 ] , [ 59, 0, 0, 59 ] , [ 59, 29, 29, 1 ] , [ 59, 58, 58, 1 ]
^ Level 90 Name Index  con   len   c2   c3  > SL(2,Z/90Z) Matrix Generators
  90A6 90 2 45 8 0 [ 1, 60, 30, 1 ] , [ 11, 0, 30, 41 ] , [ 19, 0, 0, 19 ] , [ 37, 36, 0, 73 ] , [ 46, 45, 45, 1 ] , [ 61, 0, 60, 31 ] , [ 67, 18, 66, 7 ] , [ 71, 20, 35, 1 ] , [ 73, 0, 18, 37 ] , [ 81, 50, 25, 51 ]
  90B6 108 1 54 12 0 [ 1, 45, 45, 46 ] , [ 19, 36, 36, 73 ] , [ 31, 60, 60, 61 ] , [ 41, 0, 60, 11 ] , [ 41, 55, 10, 31 ] , [ 51, 35, 10, 51 ] , [ 61, 0, 60, 31 ] , [ 69, 2, 4, 81 ] , [ 73, 54, 54, 19 ] , [ 89, 30, 60, 89 ]
  90C6 120 1 20 0 12 [ 1, 30, 0, 1 ] , [ 1, 45, 45, 46 ] , [ 19, 0, 0, 19 ] , [ 31, 40, 60, 31 ] , [ 37, 0, 18, 73 ] , [ 37, 54, 0, 73 ] , [ 55, 54, 36, 19 ] , [ 61, 30, 0, 31 ] , [ 86, 5, 75, 41 ]
^ Level 91 Name Index  con   len   c2   c3  > SL(2,Z/91Z) Matrix Generators
  91A6 98 2 98 6 2 [ 26, 81, 4, 65 ] , [ 27, 0, 0, 27 ] , [ 39, 16, 30, 52 ] , [ 39, 62, 35, 65 ] , [ 50, 21, 28, 50 ] , [ 52, 62, 87, 39 ] , [ 71, 7, 70, 71 ] , [ 78, 28, 84, 15 ] , [ 85, 7, 70, 85 ]
^ Level 100 Name Index  con   len   c2   c3  > SL(2,Z/100Z) Matrix Generators
  100A6 180 1 90 4 0 [ 1, 0, 50, 1 ] , [ 5, 32, 12, 97 ] , [ 19, 26, 83, 61 ] , [ 21, 20, 0, 81 ] , [ 21, 60, 60, 81 ] , [ 51, 0, 50, 51 ] , [ 69, 40, 80, 29 ] , [ 85, 72, 27, 17 ]
^ Level 105 Name Index  con   len   c2   c3  > SL(2,Z/105Z) Matrix Generators
  105A6 105 2 35 9 3 [ 1, 35, 35, 71 ] , [ 1, 60, 45, 76 ] , [ 15, 28, 98, 15 ] , [ 16, 30, 15, 61 ] , [ 22, 0, 0, 43 ] , [ 36, 70, 35, 36 ] , [ 46, 90, 45, 31 ] , [ 64, 0, 0, 64 ] , [ 71, 0, 0, 71 ] , [ 71, 63, 14, 8 ] , [ 76, 0, 0, 76 ] , [ 76, 90, 15, 91 ]
  105B6 105 2 35 9 3 [ 1, 35, 35, 71 ] , [ 1, 60, 45, 76 ] , [ 15, 28, 98, 15 ] , [ 16, 30, 15, 61 ] , [ 22, 0, 0, 43 ] , [ 36, 70, 35, 36 ] , [ 43, 42, 91, 1 ] , [ 46, 90, 45, 31 ] , [ 64, 0, 0, 64 ] , [ 71, 0, 0, 71 ] , [ 76, 0, 0, 76 ] , [ 76, 90, 15, 91 ]
  105C6 126 2 42 18 0 [ 1, 0, 84, 1 ] , [ 13, 10, 4, 92 ] , [ 16, 30, 15, 61 ] , [ 36, 35, 70, 36 ] , [ 46, 60, 0, 16 ] , [ 61, 90, 60, 61 ] , [ 71, 0, 0, 71 ] , [ 71, 70, 70, 1 ] , [ 76, 0, 0, 76 ] , [ 91, 45, 30, 91 ] , [ 104, 0, 0, 104 ]
^ Level 108 Name Index  con   len   c2   c3  > SL(2,Z/108Z) Matrix Generators
  108A6 144 1 24 0 18 [ 1, 0, 36, 1 ] , [ 1, 54, 54, 1 ] , [ 37, 0, 0, 73 ] , [ 55, 0, 54, 55 ] , [ 61, 18, 54, 85 ] , [ 73, 36, 84, 37 ] , [ 97, 102, 38, 1 ] , [ 103, 27, 57, 16 ] , [ 107, 0, 0, 107 ]
^ Level 121 Name Index  con   len   c2   c3  > SL(2,Z/121Z) Matrix Generators
  121A6 Γ0(121) 132 1 132 0 0 [ 21, 13, 53, 102 ] , [ 56, 55, 44, 67 ] , [ 67, 13, 74, 83 ] , [ 89, 0, 55, 34 ] , [ 120, 0, 0, 120 ]
^ Level 125 Name Index  con   len   c2   c3  > SL(2,Z/125Z) Matrix Generators
  125A6 150 1 150 2 0 [ 4, 26, 116, 98 ] , [ 11, 50, 65, 91 ] , [ 44, 45, 85, 104 ] , [ 51, 0, 75, 76 ] , [ 51, 100, 100, 76 ] , [ 61, 86, 43, 34 ] , [ 71, 65, 40, 56 ]
  125B6 150 1 150 2 0 [ 11, 50, 65, 91 ] , [ 44, 45, 85, 104 ] , [ 51, 0, 75, 76 ] , [ 51, 100, 100, 76 ] , [ 61, 86, 43, 34 ] , [ 71, 65, 40, 56 ] , [ 90, 88, 8, 12 ]
^ Level 126 Name Index  con   len   c2   c3  > SL(2,Z/126Z) Matrix Generators
  126A6 126 2 63 20 0 [ 1, 63, 63, 64 ] , [ 43, 56, 56, 29 ] , [ 43, 84, 84, 85 ] , [ 55, 0, 0, 55 ] , [ 55, 72, 90, 1 ] , [ 55, 108, 18, 1 ] , [ 55, 120, 75, 1 ] , [ 69, 64, 89, 57 ] , [ 73, 54, 108, 73 ] , [ 85, 0, 0, 43 ] , [ 113, 42, 42, 29 ]

Chris Cummins and Sebastian Pauli, computed with MAGMA