[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 2

Groups of Level: 8 9 10 11 12 13 14 15 16 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 35 36 37 38 39 40 42 44 45 48 50 54 63 64 78

^ Level 8 > 8A2 8B2 8C2 ^ Level 9 Name Index con len c2 c3 SL(2,Z/8Z) Matrix Generators 48 1 1 0 0 [ 1, 4, 4, 1 ] , [ 3, 0, 4, 3 ] , [ 7, 4, 4, 7 ] 48 1 12 0 0 [ 1, 4, 4, 1 ] , [ 4, 1, 7, 0 ] , [ 7, 4, 4, 7 ] 96 1 24 4 0 [ 0, 1, 7, 0 ] , [ 7, 0, 0, 7 ] Name Index con len c2 c3 SL(2,Z/9Z) Matrix Generators 36 1 3 0 0 [ 1, 6, 3, 1 ] , [ 7, 0, 6, 4 ] , [ 8, 0, 0, 8 ] 54 1 27 2 0 [ 1, 8, 8, 2 ] , [ 5, 3, 3, 2 ] , [ 7, 3, 3, 4 ] Name Index con len c2 c3 SL(2,Z/10Z) Matrix Generators 30 1 5 0 0 [ 3, 4, 0, 7 ] , [ 6, 5, 5, 1 ] , [ 7, 0, 2, 3 ] , [ 9, 0, 0, 9 ] 30 1 5 0 0 [ 3, 0, 8, 7 ] , [ 7, 6, 0, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] 60 1 15 4 0 [ 6, 5, 5, 1 ] , [ 7, 4, 5, 3 ] , [ 9, 0, 0, 9 ] 60 1 30 0 0 [ 1, 0, 5, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] 60 1 30 4 0 [ 7, 0, 9, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] 90 1 45 2 0 [ 1, 0, 5, 1 ] , [ 7, 4, 5, 3 ] , [ 9, 0, 0, 9 ] Name Index con len c2 c3 SL(2,Z/11Z) Matrix Generators 66 1 66 6 0 [ 1, 8, 7, 2 ] , [ 8, 5, 9, 3 ] , [ 10, 0, 0, 10 ] Name Index con len c2 c3 SL(2,Z/12Z) Matrix Generators 24 1 4 0 0 [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 9, 4, 8, 9 ] , [ 9, 8, 4, 9 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 0, 11 ] 36 1 3 0 0 [ 1, 6, 6, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 8, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 7, 10, 10, 11 ] , [ 9, 8, 4, 9 ] 36 1 9 0 0 [ 1, 6, 6, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 2, 1 ] , [ 7, 6, 6, 7 ] , [ 10, 9, 3, 10 ] , [ 11, 0, 0, 11 ] , [ 11, 8, 2, 7 ] 36 1 9 0 0 [ 0, 5, 7, 6 ] , [ 1, 6, 6, 1 ] , [ 4, 1, 7, 2 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] 36 1 9 0 0 [ 1, 6, 6, 1 ] , [ 3, 4, 2, 3 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 5, 8, 2, 1 ] , [ 7, 6, 6, 7 ] , [ 9, 4, 2, 9 ] 48 1 4 0 0 [ 1, 6, 6, 1 ] , [ 3, 4, 8, 7 ] , [ 5, 4, 8, 9 ] , [ 7, 6, 0, 7 ] , [ 9, 8, 4, 5 ] 48 1 24 0 0 [ 1, 0, 8, 1 ] , [ 4, 9, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 0, 4, 5 ] , [ 7, 0, 0, 7 ] , [ 11, 0, 8, 11 ] 72 1 18 8 0 [ 5, 0, 0, 5 ] , [ 6, 11, 1, 6 ] , [ 7, 0, 0, 7 ] , [ 8, 5, 11, 4 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 10, 7 ] 72 1 18 8 0 [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 8, 1, 7, 4 ] , [ 9, 8, 4, 9 ] Name Index con len c2 c3 SL(2,Z/13Z) Matrix Generators Γ1(13) 84 1 14 0 0 [ 6, 11, 6, 9 ] , [ 11, 9, 12, 4 ] , [ 12, 0, 0, 12 ] Name Index con len c2 c3 SL(2,Z/14Z) Matrix Generators 42 2 21 2 0 [ 1, 7, 0, 1 ] , [ 7, 10, 2, 13 ] , [ 7, 12, 4, 7 ] , [ 9, 6, 12, 5 ] , [ 13, 0, 0, 13 ] 42 2 21 4 0 [ 0, 5, 11, 0 ] , [ 1, 9, 4, 9 ] , [ 2, 13, 5, 5 ] , [ 8, 7, 7, 1 ] , [ 13, 7, 7, 6 ] 42 2 21 4 0 [ 7, 10, 2, 13 ] , [ 7, 12, 4, 7 ] , [ 9, 5, 10, 1 ] , [ 9, 6, 12, 5 ] , [ 13, 0, 0, 13 ] 48 1 8 0 0 [ 5, 6, 2, 11 ] , [ 8, 7, 7, 1 ] , [ 9, 8, 12, 3 ] , [ 11, 8, 12, 5 ] 48 1 8 0 0 [ 3, 0, 6, 5 ] , [ 3, 10, 8, 13 ] , [ 11, 8, 12, 5 ] , [ 13, 10, 2, 7 ] 63 1 63 5 0 [ 1, 0, 7, 1 ] , [ 1, 2, 11, 9 ] , [ 7, 12, 4, 7 ] , [ 9, 6, 12, 5 ] , [ 13, 0, 0, 13 ] Name Index con len c2 c3 SL(2,Z/15Z) Matrix Generators 30 1 15 2 0 [ 4, 0, 0, 4 ] , [ 6, 10, 5, 6 ] , [ 7, 0, 12, 13 ] , [ 7, 6, 0, 13 ] , [ 11, 0, 0, 11 ] , [ 13, 6, 12, 1 ] 36 1 6 0 0 [ 1, 10, 10, 11 ] , [ 6, 10, 5, 6 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 0, 11 ] , [ 14, 0, 0, 14 ] 40 1 40 0 1 [ 1, 0, 10, 1 ] , [ 4, 0, 10, 4 ] , [ 4, 3, 3, 10 ] , [ 7, 9, 5, 13 ] , [ 11, 0, 0, 11 ] 60 1 30 8 0 [ 2, 10, 4, 13 ] , [ 4, 0, 0, 4 ] , [ 6, 10, 5, 6 ] , [ 10, 12, 12, 4 ] , [ 11, 0, 0, 11 ] 60 2 60 4 3 [ 2, 10, 7, 13 ] , [ 4, 0, 0, 4 ] , [ 4, 9, 1, 10 ] , [ 6, 8, 1, 9 ] , [ 11, 0, 0, 11 ] Name Index con len c2 c3 SL(2,Z/16Z) Matrix Generators 24 1 3 0 0 [ 0, 7, 9, 8 ] , [ 1, 8, 8, 1 ] , [ 1, 10, 10, 5 ] , [ 5, 4, 4, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 6, 6, 15 ] , [ 15, 0, 0, 15 ] , [ 15, 12, 12, 15 ] 24 1 12 0 0 [ 0, 13, 11, 12 ] , [ 1, 8, 8, 1 ] , [ 5, 4, 4, 13 ] , [ 5, 10, 10, 1 ] , [ 7, 4, 12, 7 ] , [ 7, 6, 14, 3 ] , [ 9, 8, 8, 9 ] , [ 11, 14, 14, 15 ] , [ 15, 12, 4, 15 ] 48 1 3 0 0 [ 1, 4, 0, 1 ] , [ 1, 8, 0, 1 ] , [ 3, 12, 8, 11 ] , [ 5, 14, 0, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 8, 9 ] , [ 9, 8, 0, 9 ] 48 1 12 0 0 [ 1, 8, 8, 1 ] , [ 4, 7, 9, 8 ] , [ 5, 0, 0, 13 ] , [ 8, 7, 9, 12 ] , [ 9, 8, 8, 9 ] , [ 15, 4, 12, 15 ] 48 1 12 4 0 [ 3, 8, 0, 11 ] , [ 7, 12, 4, 7 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 12, 9, 7, 12 ] , [ 15, 0, 0, 15 ] 48 2 12 4 0 [ 1, 8, 8, 1 ] , [ 9, 8, 8, 9 ] , [ 11, 2, 10, 15 ] , [ 13, 4, 4, 5 ] , [ 13, 12, 12, 5 ] , [ 14, 11, 1, 2 ] , [ 15, 0, 0, 15 ] 64 1 64 8 1 [ 0, 1, 15, 0 ] , [ 0, 9, 7, 0 ] , [ 2, 11, 11, 13 ] , [ 8, 5, 3, 8 ] , [ 8, 13, 11, 8 ] , [ 9, 0, 0, 9 ] , [ 15, 0, 0, 15 ] 64 2 32 4 4 [ 0, 1, 15, 8 ] , [ 1, 8, 8, 1 ] , [ 7, 0, 8, 7 ] , [ 9, 0, 8, 9 ] , [ 9, 8, 0, 9 ] , [ 10, 3, 11, 5 ] , [ 15, 0, 0, 15 ] 96 1 12 0 0 [ 1, 0, 4, 1 ] , [ 1, 0, 8, 1 ] , [ 1, 4, 4, 1 ] , [ 1, 8, 8, 1 ] , [ 15, 8, 8, 15 ] Γ1(16) 96 1 24 0 0 [ 1, 2, 14, 13 ] , [ 2, 9, 7, 0 ] , [ 5, 4, 12, 13 ] , [ 9, 8, 8, 9 ] , [ 11, 10, 6, 7 ] , [ 13, 14, 2, 1 ] 96 1 24 0 0 [ 1, 8, 0, 1 ] , [ 3, 10, 0, 11 ] , [ 9, 12, 0, 9 ] , [ 13, 2, 8, 5 ] , [ 13, 6, 0, 5 ] , [ 13, 10, 8, 5 ] 96 1 24 4 0 [ 0, 1, 15, 0 ] , [ 0, 15, 1, 0 ] , [ 5, 4, 12, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 15, 0, 0, 15 ] , [ 15, 8, 8, 15 ] Name Index con len c2 c3 SL(2,Z/18Z) Matrix Generators 18 1 9 0 0 [ 1, 9, 9, 10 ] , [ 1, 16, 10, 17 ] , [ 5, 12, 12, 11 ] , [ 7, 0, 0, 13 ] , [ 9, 10, 8, 9 ] , [ 13, 6, 6, 7 ] 24 1 4 0 0 [ 1, 0, 6, 1 ] , [ 10, 9, 9, 1 ] , [ 13, 0, 12, 7 ] , [ 13, 6, 8, 1 ] , [ 17, 0, 0, 17 ] 24 1 8 0 0 [ 1, 0, 6, 1 ] , [ 1, 3, 3, 10 ] , [ 4, 3, 1, 1 ] , [ 13, 0, 12, 7 ] , [ 17, 0, 0, 17 ] 36 1 12 0 0 [ 1, 0, 6, 1 ] , [ 1, 12, 2, 7 ] , [ 10, 9, 9, 10 ] , [ 13, 0, 12, 7 ] , [ 17, 0, 0, 17 ] 36 1 12 0 0 [ 1, 0, 6, 1 ] , [ 1, 0, 9, 1 ] , [ 13, 0, 12, 7 ] , [ 13, 6, 8, 1 ] , [ 17, 0, 0, 17 ] 36 1 18 0 0 [ 1, 12, 0, 1 ] , [ 7, 15, 3, 4 ] , [ 11, 6, 6, 5 ] , [ 13, 0, 6, 7 ] , [ 17, 16, 4, 7 ] 36 2 9 4 0 [ 1, 9, 9, 10 ] , [ 1, 16, 1, 17 ] , [ 7, 3, 3, 4 ] , [ 7, 9, 9, 4 ] , [ 10, 9, 9, 1 ] , [ 17, 0, 0, 17 ] 36 2 18 4 0 [ 1, 12, 6, 1 ] , [ 3, 4, 11, 3 ] , [ 7, 9, 15, 4 ] , [ 7, 12, 0, 13 ] , [ 17, 6, 12, 17 ] 54 1 9 6 0 [ 5, 0, 12, 11 ] , [ 7, 0, 12, 13 ] , [ 7, 12, 0, 13 ] , [ 11, 10, 4, 7 ] , [ 13, 0, 15, 7 ] 54 1 27 0 6 [ 1, 9, 9, 10 ] , [ 1, 12, 2, 7 ] , [ 1, 14, 14, 17 ] , [ 5, 8, 8, 13 ] , [ 17, 0, 0, 17 ] 54 2 27 8 0 [ 0, 1, 17, 0 ] , [ 1, 16, 10, 17 ] , [ 5, 12, 12, 11 ] , [ 7, 12, 12, 13 ] , [ 10, 9, 9, 1 ] 54 2 27 8 0 [ 5, 0, 12, 11 ] , [ 7, 0, 12, 13 ] , [ 7, 12, 0, 13 ] , [ 11, 8, 17, 1 ] , [ 15, 14, 16, 9 ] 54 2 54 8 0 [ 5, 12, 12, 11 ] , [ 7, 12, 12, 13 ] , [ 9, 10, 17, 9 ] , [ 11, 10, 1, 1 ] , [ 16, 9, 9, 13 ] 72 1 12 0 6 [ 1, 0, 6, 1 ] , [ 1, 12, 2, 7 ] , [ 10, 9, 9, 1 ] , [ 17, 0, 0, 17 ] 72 1 24 0 6 [ 1, 0, 6, 1 ] , [ 16, 9, 15, 13 ] , [ 16, 15, 7, 1 ] , [ 17, 0, 0, 17 ] 108 1 18 0 0 [ 1, 0, 9, 1 ] , [ 13, 0, 0, 7 ] , [ 13, 12, 6, 7 ] , [ 17, 0, 0, 17 ] Γ1(18) 108 1 36 0 0 [ 1, 0, 6, 1 ] , [ 1, 0, 9, 1 ] , [ 7, 0, 2, 13 ] , [ 17, 0, 0, 17 ] Name Index con len c2 c3 SL(2,Z/19Z) Matrix Generators 57 2 57 5 3 [ 11, 18, 16, 9 ] , [ 14, 3, 4, 5 ] , [ 18, 0, 0, 18 ] Name Index con len c2 c3 SL(2,Z/20Z) Matrix Generators 30 1 15 0 0 [ 1, 0, 10, 1 ] , [ 1, 0, 15, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 10, 11 ] , [ 13, 0, 8, 17 ] , [ 17, 16, 0, 13 ] 30 1 15 2 0 [ 1, 0, 10, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 10, 11 ] , [ 11, 10, 15, 1 ] , [ 13, 0, 8, 17 ] , [ 17, 16, 0, 13 ] 36 1 18 0 0 [ 1, 0, 10, 1 ] , [ 5, 12, 12, 17 ] , [ 9, 0, 0, 9 ] , [ 9, 18, 16, 1 ] , [ 11, 0, 10, 11 ] , [ 15, 2, 17, 17 ] 40 1 20 0 4 [ 6, 15, 15, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 0, 11 ] , [ 13, 0, 8, 17 ] , [ 17, 16, 0, 13 ] 40 1 40 4 1 [ 1, 10, 5, 11 ] , [ 1, 15, 15, 6 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 0, 11 ] , [ 17, 14, 5, 3 ] , [ 19, 0, 0, 19 ] 60 1 30 4 0 [ 1, 0, 10, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 10, 11 ] , [ 17, 10, 4, 13 ] , [ 17, 10, 9, 3 ] Name Index con len c2 c3 SL(2,Z/21Z) Matrix Generators 24 1 8 0 0 [ 1, 0, 18, 1 ] , [ 1, 14, 14, 8 ] , [ 8, 0, 0, 8 ] , [ 8, 14, 14, 1 ] , [ 13, 0, 0, 13 ] , [ 16, 0, 0, 4 ] , [ 20, 0, 6, 20 ] 28 2 28 0 1 [ 1, 18, 3, 13 ] , [ 7, 3, 9, 7 ] , [ 7, 15, 6, 13 ] , [ 8, 0, 0, 8 ] , [ 10, 15, 18, 4 ] , [ 13, 0, 0, 13 ] , [ 15, 7, 14, 8 ] , [ 20, 17, 4, 15 ] 42 2 7 6 0 [ 4, 6, 3, 10 ] , [ 4, 18, 0, 16 ] , [ 7, 18, 12, 7 ] , [ 8, 0, 0, 8 ] , [ 8, 7, 7, 1 ] , [ 8, 14, 14, 1 ] , [ 13, 0, 0, 13 ] 42 2 21 6 0 [ 4, 6, 3, 10 ] , [ 4, 18, 0, 16 ] , [ 7, 18, 12, 7 ] , [ 8, 0, 0, 8 ] , [ 8, 7, 7, 1 ] , [ 13, 0, 0, 13 ] , [ 16, 12, 6, 19 ] Name Index con len c2 c3 SL(2,Z/22Z) Matrix Generators 24 1 12 0 0 [ 12, 11, 11, 1 ] , [ 15, 14, 2, 21 ] , [ 19, 1, 17, 16 ] , [ 19, 12, 6, 5 ] , [ 21, 0, 0, 21 ] 33 2 33 3 0 [ 1, 0, 11, 1 ] , [ 11, 2, 16, 21 ] , [ 11, 8, 4, 11 ] , [ 21, 0, 0, 21 ] Γ0(22) 36 1 36 0 0 [ 1, 0, 11, 1 ] , [ 15, 14, 2, 21 ] , [ 19, 12, 6, 5 ] , [ 21, 0, 0, 21 ] Name Index con len c2 c3 SL(2,Z/23Z) Matrix Generators Γ0(23) 24 1 24 0 0 [ 12, 14, 4, 22 ] , [ 21, 1, 14, 4 ] , [ 22, 0, 0, 22 ] Name Index con len c2 c3 SL(2,Z/24Z) Matrix Generators 32 2 16 0 2 [ 1, 6, 15, 19 ] , [ 1, 16, 0, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 21, 1 ] , [ 13, 0, 12, 13 ] , [ 13, 9, 9, 10 ] , [ 13, 12, 0, 13 ] , [ 17, 16, 0, 17 ] , [ 19, 22, 21, 13 ] 36 1 6 0 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 12, 3, 13 ] , [ 7, 0, 18, 7 ] , [ 9, 16, 20, 9 ] , [ 13, 0, 12, 13 ] , [ 13, 8, 20, 5 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 12, 3, 7 ] , [ 21, 8, 22, 21 ] 36 1 9 4 0 [ 1, 0, 12, 1 ] , [ 1, 16, 10, 17 ] , [ 7, 0, 0, 7 ] , [ 9, 8, 16, 9 ] , [ 13, 0, 12, 13 ] , [ 13, 12, 6, 13 ] , [ 13, 12, 18, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 18, 3, 13 ] 36 1 18 0 0 [ 1, 0, 12, 1 ] , [ 1, 0, 15, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 16, 10, 17 ] , [ 3, 4, 23, 15 ] , [ 7, 0, 18, 7 ] , [ 7, 20, 11, 11 ] , [ 13, 0, 9, 13 ] , [ 13, 0, 12, 13 ] , [ 13, 20, 8, 5 ] , [ 17, 0, 0, 17 ] 48 1 8 0 6 [ 1, 12, 12, 1 ] , [ 1, 16, 16, 17 ] , [ 9, 16, 8, 9 ] , [ 13, 12, 0, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 22, 15, 19, 1 ] 48 1 12 0 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 8, 0, 1 ] , [ 1, 12, 3, 13 ] , [ 7, 12, 6, 7 ] , [ 13, 0, 0, 13 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 9, 17 ] , [ 23, 0, 0, 23 ] 48 1 12 8 0 [ 1, 12, 12, 1 ] , [ 3, 20, 4, 3 ] , [ 7, 0, 0, 7 ] , [ 13, 9, 9, 10 ] , [ 13, 12, 0, 13 ] , [ 16, 17, 23, 8 ] , [ 17, 12, 12, 17 ] , [ 21, 8, 16, 21 ] 48 1 12 8 0 [ 0, 17, 7, 12 ] , [ 1, 12, 12, 1 ] , [ 1, 16, 4, 17 ] , [ 7, 0, 0, 7 ] , [ 13, 9, 9, 10 ] , [ 13, 12, 0, 13 ] , [ 17, 12, 12, 17 ] 48 1 24 0 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 16, 0, 1 ] , [ 7, 0, 12, 7 ] , [ 7, 16, 12, 7 ] , [ 11, 8, 0, 11 ] , [ 13, 0, 0, 13 ] , [ 13, 22, 15, 7 ] , [ 19, 0, 12, 19 ] , [ 19, 8, 6, 19 ] 48 1 24 0 6 [ 1, 12, 12, 1 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 12, 7 ] , [ 11, 20, 2, 19 ] , [ 13, 0, 12, 13 ] , [ 13, 14, 14, 17 ] , [ 13, 15, 7, 10 ] , [ 17, 10, 10, 13 ] 48 2 12 8 0 [ 0, 17, 7, 12 ] , [ 1, 12, 12, 1 ] , [ 4, 13, 19, 20 ] , [ 5, 16, 4, 13 ] , [ 7, 0, 0, 7 ] , [ 13, 9, 9, 10 ] , [ 13, 12, 0, 13 ] , [ 17, 12, 12, 17 ] 72 1 6 12 0 [ 1, 12, 12, 1 ] , [ 4, 3, 21, 4 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 0, 13 ] , [ 15, 20, 4, 15 ] , [ 17, 0, 0, 17 ] , [ 19, 12, 12, 19 ] , [ 19, 20, 20, 11 ] , [ 23, 0, 0, 23 ] 72 1 12 12 0 [ 1, 0, 12, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 0, 12, 7 ] , [ 7, 12, 6, 7 ] , [ 7, 12, 18, 7 ] , [ 7, 18, 3, 1 ] , [ 15, 16, 8, 15 ] , [ 17, 0, 0, 17 ] , [ 17, 8, 8, 1 ] 72 1 18 8 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 7, 2, 17, 5 ] , [ 7, 2, 23, 17 ] , [ 11, 14, 23, 1 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] 72 1 18 8 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 9, 8, 16, 9 ] , [ 9, 8, 22, 9 ] , [ 11, 14, 23, 1 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] 72 1 18 12 0 [ 1, 0, 12, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 0, 12, 7 ] , [ 9, 8, 4, 9 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 6, 9, 13 ] , [ 19, 20, 2, 11 ] , [ 23, 0, 0, 23 ] 72 1 36 12 0 [ 1, 0, 12, 1 ] , [ 3, 4, 2, 3 ] , [ 7, 0, 0, 7 ] , [ 7, 8, 8, 23 ] , [ 7, 12, 6, 7 ] , [ 7, 12, 18, 7 ] , [ 7, 18, 3, 1 ] , [ 17, 0, 0, 17 ] , [ 21, 4, 14, 21 ] Name Index con len c2 c3 SL(2,Z/25Z) Matrix Generators 30 1 30 2 0 [ 6, 10, 20, 21 ] , [ 9, 11, 18, 11 ] , [ 10, 2, 22, 12 ] , [ 11, 0, 10, 16 ] , [ 24, 0, 0, 24 ] 30 1 30 2 0 [ 6, 10, 20, 21 ] , [ 7, 13, 18, 5 ] , [ 9, 11, 18, 11 ] , [ 11, 0, 10, 16 ] , [ 24, 0, 0, 24 ] 30 1 30 2 0 [ 6, 10, 20, 21 ] , [ 9, 11, 18, 11 ] , [ 11, 0, 10, 16 ] , [ 12, 8, 23, 5 ] , [ 24, 0, 0, 24 ] 30 1 30 2 0 [ 4, 19, 9, 18 ] , [ 6, 10, 20, 21 ] , [ 9, 11, 18, 11 ] , [ 11, 0, 10, 16 ] , [ 24, 0, 0, 24 ] 50 1 50 2 5 [ 2, 4, 15, 18 ] , [ 9, 18, 13, 15 ] , [ 14, 5, 0, 9 ] , [ 16, 15, 15, 11 ] , [ 21, 0, 15, 6 ] 75 1 75 7 0 [ 1, 0, 10, 1 ] , [ 6, 15, 5, 21 ] , [ 13, 14, 15, 22 ] , [ 19, 10, 0, 4 ] , [ 22, 20, 17, 3 ] Name Index con len c2 c3 SL(2,Z/26Z) Matrix Generators Γ0(26) 42 1 42 2 0 [ 1, 0, 13, 1 ] , [ 5, 20, 16, 7 ] , [ 11, 14, 16, 11 ] , [ 13, 16, 4, 15 ] , [ 17, 0, 24, 23 ] 84 1 14 12 0 [ 1, 13, 13, 14 ] , [ 17, 3, 16, 9 ] , [ 19, 24, 6, 9 ] , [ 25, 0, 0, 25 ] Name Index con len c2 c3 SL(2,Z/27Z) Matrix Generators 36 1 12 0 0 [ 1, 0, 18, 1 ] , [ 10, 0, 0, 19 ] , [ 10, 0, 24, 19 ] , [ 13, 9, 1, 7 ] , [ 22, 0, 0, 16 ] , [ 26, 0, 0, 26 ] 36 1 12 0 3 [ 1, 0, 18, 1 ] , [ 1, 18, 6, 1 ] , [ 10, 0, 9, 19 ] , [ 13, 12, 8, 22 ] , [ 19, 0, 0, 10 ] , [ 19, 3, 17, 7 ] , [ 26, 0, 0, 26 ] Name Index con len c2 c3 SL(2,Z/28Z) Matrix Generators 32 1 32 0 2 [ 1, 7, 7, 22 ] , [ 13, 12, 12, 9 ] , [ 13, 24, 16, 21 ] , [ 15, 0, 0, 15 ] , [ 15, 14, 7, 1 ] , [ 25, 8, 12, 5 ] 42 2 21 4 0 [ 1, 7, 0, 1 ] , [ 1, 14, 0, 1 ] , [ 9, 12, 10, 1 ] , [ 9, 20, 12, 5 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 0, 15 ] , [ 21, 12, 4, 21 ] , [ 21, 24, 16, 13 ] 42 2 21 6 0 [ 1, 7, 14, 15 ] , [ 1, 14, 0, 1 ] , [ 9, 12, 24, 1 ] , [ 9, 20, 12, 5 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 0, 15 ] , [ 21, 12, 4, 21 ] , [ 21, 24, 16, 13 ] Γ0(28) 48 1 24 0 0 [ 1, 0, 14, 1 ] , [ 1, 0, 21, 1 ] , [ 13, 24, 16, 21 ] , [ 15, 0, 14, 15 ] , [ 17, 0, 20, 5 ] , [ 17, 24, 8, 13 ] , [ 25, 8, 12, 5 ] 56 2 28 8 2 [ 9, 20, 12, 5 ] , [ 13, 0, 0, 13 ] , [ 15, 0, 0, 15 ] , [ 21, 12, 4, 21 ] , [ 21, 24, 16, 13 ] , [ 22, 21, 21, 1 ] , [ 23, 19, 10, 1 ] 96 1 16 0 12 [ 1, 14, 14, 1 ] , [ 9, 12, 4, 21 ] , [ 13, 4, 20, 17 ] , [ 13, 14, 0, 13 ] , [ 15, 0, 14, 15 ] , [ 27, 27, 1, 0 ] Name Index con len c2 c3 SL(2,Z/29Z) Matrix Generators Γ0(29) 30 1 30 2 0 [ 2, 13, 13, 27 ] , [ 2, 19, 3, 0 ] , [ 3, 20, 20, 8 ] , [ 28, 0, 0, 28 ] Name Index con len c2 c3 SL(2,Z/30Z) Matrix Generators 30 1 15 4 0 [ 1, 15, 15, 16 ] , [ 7, 21, 15, 28 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 25, 1 ] , [ 13, 6, 12, 1 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 5, 21 ] , [ 22, 15, 27, 13 ] 30 2 10 0 3 [ 1, 10, 10, 11 ] , [ 1, 20, 20, 11 ] , [ 1, 24, 28, 13 ] , [ 7, 6, 0, 13 ] , [ 11, 0, 0, 11 ] , [ 19, 0, 0, 19 ] , [ 19, 12, 24, 1 ] , [ 21, 10, 20, 21 ] , [ 28, 21, 27, 1 ] 36 1 18 4 0 [ 1, 25, 10, 11 ] , [ 7, 18, 18, 25 ] , [ 11, 0, 0, 11 ] , [ 16, 15, 15, 1 ] , [ 21, 10, 20, 21 ] , [ 27, 25, 2, 3 ] , [ 29, 0, 0, 29 ] 40 1 20 0 4 [ 1, 15, 15, 16 ] , [ 13, 0, 6, 7 ] , [ 15, 8, 28, 29 ] , [ 19, 0, 0, 19 ] , [ 19, 6, 18, 1 ] , [ 21, 10, 20, 1 ] , [ 21, 20, 10, 11 ] 54 1 18 6 0 [ 1, 10, 10, 11 ] , [ 1, 15, 0, 1 ] , [ 7, 18, 18, 25 ] , [ 11, 0, 0, 11 ] , [ 21, 10, 20, 21 ] , [ 27, 10, 2, 3 ] , [ 29, 0, 0, 29 ] 60 1 10 12 0 [ 1, 15, 15, 16 ] , [ 7, 0, 9, 13 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 10, 1 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 20, 21 ] , [ 25, 12, 12, 19 ] Name Index con len c2 c3 SL(2,Z/31Z) Matrix Generators Γ0(31) 32 1 32 0 2 [ 6, 25, 3, 23 ] , [ 14, 9, 3, 2 ] , [ 17, 3, 1, 13 ] , [ 30, 0, 0, 30 ] Name Index con len c2 c3 SL(2,Z/32Z) Matrix Generators 48 1 6 0 0 [ 1, 16, 16, 1 ] , [ 1, 28, 28, 17 ] , [ 5, 20, 12, 29 ] , [ 9, 8, 24, 25 ] , [ 9, 24, 8, 25 ] , [ 11, 26, 6, 23 ] , [ 13, 4, 12, 21 ] , [ 17, 10, 6, 13 ] , [ 17, 16, 16, 17 ] , [ 18, 21, 3, 0 ] , [ 19, 26, 22, 15 ] , [ 23, 10, 30, 27 ] 96 1 12 0 0 [ 1, 16, 0, 1 ] , [ 1, 24, 0, 1 ] , [ 9, 8, 16, 25 ] , [ 17, 12, 0, 17 ] , [ 17, 16, 0, 17 ] , [ 17, 20, 0, 17 ] , [ 21, 0, 24, 29 ] , [ 21, 6, 24, 13 ] , [ 23, 10, 16, 7 ] , [ 25, 8, 16, 9 ] , [ 29, 28, 8, 21 ] 96 1 24 0 0 [ 1, 18, 14, 29 ] , [ 1, 26, 6, 29 ] , [ 5, 14, 18, 25 ] , [ 5, 28, 4, 29 ] , [ 9, 8, 24, 25 ] , [ 11, 26, 6, 23 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 17 ] , [ 21, 20, 12, 13 ] , [ 28, 13, 19, 2 ] Name Index con len c2 c3 SL(2,Z/35Z) Matrix Generators 35 2 35 3 2 [ 1, 25, 10, 6 ] , [ 6, 0, 0, 6 ] , [ 15, 21, 14, 15 ] , [ 20, 3, 18, 15 ] , [ 21, 10, 30, 21 ] , [ 21, 15, 20, 6 ] , [ 27, 28, 14, 34 ] , [ 29, 0, 0, 29 ] , [ 31, 15, 25, 11 ] 40 1 40 0 4 [ 1, 0, 25, 1 ] , [ 6, 0, 0, 6 ] , [ 6, 21, 34, 20 ] , [ 16, 0, 0, 11 ] , [ 22, 0, 34, 8 ] , [ 27, 28, 20, 13 ] , [ 29, 0, 0, 29 ] 42 2 42 6 0 [ 1, 0, 7, 1 ] , [ 1, 25, 10, 6 ] , [ 6, 0, 0, 6 ] , [ 13, 10, 4, 22 ] , [ 21, 10, 30, 21 ] , [ 21, 15, 20, 6 ] , [ 29, 0, 0, 29 ] , [ 31, 15, 25, 11 ] Name Index con len c2 c3 SL(2,Z/36Z) Matrix Generators 48 1 8 0 6 [ 1, 0, 24, 1 ] , [ 1, 18, 18, 1 ] , [ 10, 3, 35, 25 ] , [ 13, 0, 12, 25 ] , [ 13, 12, 16, 1 ] , [ 19, 0, 18, 19 ] , [ 35, 0, 0, 35 ] 54 1 27 10 0 [ 1, 0, 18, 1 ] , [ 15, 32, 34, 27 ] , [ 19, 0, 18, 19 ] , [ 19, 28, 10, 11 ] , [ 23, 0, 30, 11 ] , [ 25, 0, 12, 13 ] , [ 25, 12, 0, 13 ] , [ 33, 10, 17, 15 ] 54 2 27 8 0 [ 1, 0, 18, 1 ] , [ 13, 0, 15, 25 ] , [ 15, 28, 35, 15 ] , [ 19, 0, 18, 19 ] , [ 23, 0, 30, 11 ] , [ 25, 0, 12, 13 ] , [ 25, 12, 0, 13 ] , [ 29, 10, 22, 25 ] 72 2 36 16 0 [ 1, 24, 12, 1 ] , [ 9, 20, 4, 9 ] , [ 10, 27, 27, 1 ] , [ 13, 0, 24, 25 ] , [ 19, 0, 0, 19 ] , [ 20, 1, 31, 16 ] , [ 29, 12, 12, 5 ] Name Index con len c2 c3 SL(2,Z/37Z) Matrix Generators Γ0(37) 38 1 38 2 2 [ 2, 18, 18, 33 ] , [ 17, 1, 2, 35 ] , [ 17, 4, 8, 15 ] , [ 19, 2, 4, 18 ] , [ 36, 0, 0, 36 ] Name Index con len c2 c3 SL(2,Z/38Z) Matrix Generators 40 1 20 0 4 [ 20, 19, 19, 1 ] , [ 21, 10, 36, 19 ] , [ 29, 12, 26, 37 ] , [ 31, 10, 28, 25 ] , [ 37, 0, 0, 37 ] Name Index con len c2 c3 SL(2,Z/39Z) Matrix Generators 42 1 14 6 0 [ 1, 26, 26, 14 ] , [ 4, 0, 24, 10 ] , [ 13, 3, 30, 28 ] , [ 14, 0, 0, 14 ] , [ 14, 26, 26, 1 ] , [ 27, 26, 13, 27 ] , [ 31, 33, 3, 7 ] , [ 37, 27, 3, 37 ] Name Index con len c2 c3 SL(2,Z/40Z) Matrix Generators 40 2 20 2 4 [ 6, 15, 35, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 32, 24, 1 ] , [ 16, 15, 25, 16 ] , [ 17, 8, 16, 17 ] , [ 21, 0, 20, 21 ] , [ 21, 20, 0, 21 ] , [ 31, 20, 20, 31 ] , [ 33, 0, 8, 17 ] Name Index con len c2 c3 SL(2,Z/42Z) Matrix Generators 42 2 21 8 0 [ 7, 12, 18, 7 ] , [ 7, 24, 30, 13 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 7, 15 ] , [ 22, 21, 21, 1 ] , [ 27, 26, 10, 33 ] , [ 29, 0, 0, 29 ] , [ 29, 14, 35, 1 ] , [ 37, 6, 12, 19 ] 48 1 16 0 6 [ 8, 21, 7, 29 ] , [ 13, 0, 0, 13 ] , [ 13, 6, 36, 7 ] , [ 15, 14, 28, 15 ] , [ 25, 8, 26, 5 ] , [ 29, 0, 0, 29 ] , [ 29, 28, 28, 1 ] , [ 31, 24, 36, 13 ] 48 2 8 0 6 [ 1, 21, 21, 22 ] , [ 7, 18, 40, 13 ] , [ 13, 18, 6, 31 ] , [ 29, 0, 0, 29 ] , [ 29, 14, 14, 1 ] , [ 39, 22, 26, 33 ] , [ 41, 28, 28, 13 ] Name Index con len c2 c3 SL(2,Z/44Z) Matrix Generators 44 2 44 6 2 [ 21, 0, 0, 21 ] , [ 22, 13, 5, 43 ] , [ 23, 0, 0, 23 ] , [ 23, 22, 33, 1 ] , [ 33, 8, 4, 33 ] , [ 34, 11, 11, 1 ] Name Index con len c2 c3 SL(2,Z/45Z) Matrix Generators 54 1 54 10 0 [ 1, 15, 30, 1 ] , [ 10, 18, 18, 37 ] , [ 11, 15, 15, 41 ] , [ 16, 0, 15, 31 ] , [ 16, 15, 0, 31 ] , [ 21, 25, 5, 36 ] , [ 24, 2, 4, 36 ] , [ 31, 0, 30, 16 ] , [ 31, 10, 10, 41 ] , [ 31, 15, 15, 16 ] , [ 44, 30, 15, 44 ] Name Index con len c2 c3 SL(2,Z/48Z) Matrix Generators 72 1 9 16 0 [ 1, 0, 24, 1 ] , [ 11, 14, 41, 13 ] , [ 13, 20, 38, 29 ] , [ 17, 0, 0, 17 ] , [ 17, 32, 32, 1 ] , [ 23, 0, 24, 23 ] , [ 25, 0, 24, 25 ] , [ 25, 4, 46, 17 ] , [ 25, 20, 2, 17 ] , [ 41, 24, 36, 41 ] Name Index con len c2 c3 SL(2,Z/50Z) Matrix Generators 60 1 30 4 0 [ 7, 48, 18, 45 ] , [ 19, 0, 20, 29 ] , [ 26, 25, 25, 1 ] , [ 31, 0, 30, 21 ] , [ 31, 40, 40, 21 ] , [ 41, 0, 40, 11 ] , [ 43, 40, 23, 47 ] Γ0(50) 90 1 90 2 0 [ 1, 0, 25, 1 ] , [ 7, 48, 18, 45 ] , [ 19, 0, 20, 29 ] , [ 31, 0, 30, 21 ] , [ 31, 40, 40, 21 ] , [ 41, 0, 40, 11 ] , [ 43, 40, 48, 47 ] Name Index con len c2 c3 SL(2,Z/54Z) Matrix Generators 72 1 12 0 12 [ 1, 0, 18, 1 ] , [ 1, 27, 27, 28 ] , [ 19, 0, 18, 37 ] , [ 19, 18, 42, 37 ] , [ 31, 0, 0, 7 ] , [ 37, 0, 0, 19 ] , [ 37, 42, 52, 43 ] , [ 53, 0, 0, 53 ] 108 1 36 0 0 [ 1, 0, 27, 1 ] , [ 1, 0, 36, 1 ] , [ 7, 18, 42, 31 ] , [ 7, 18, 46, 49 ] , [ 35, 0, 0, 17 ] , [ 37, 0, 36, 19 ] , [ 37, 0, 48, 19 ] Name Index con len c2 c3 SL(2,Z/63Z) Matrix Generators 63 2 63 15 0 [ 8, 35, 56, 1 ] , [ 22, 0, 21, 43 ] , [ 22, 42, 42, 43 ] , [ 28, 18, 54, 28 ] , [ 29, 7, 7, 43 ] , [ 29, 42, 42, 50 ] , [ 37, 54, 27, 19 ] , [ 46, 18, 0, 37 ] , [ 46, 27, 45, 10 ] , [ 55, 0, 0, 55 ] Name Index con len c2 c3 SL(2,Z/64Z) Matrix Generators 96 1 24 0 0 [ 1, 32, 32, 1 ] , [ 1, 48, 48, 1 ] , [ 9, 48, 0, 57 ] , [ 9, 56, 40, 57 ] , [ 13, 60, 36, 53 ] , [ 17, 48, 16, 49 ] , [ 21, 2, 22, 57 ] , [ 25, 56, 8, 41 ] , [ 29, 44, 52, 37 ] , [ 33, 32, 32, 33 ] , [ 39, 62, 18, 27 ] , [ 42, 29, 59, 24 ] , [ 55, 16, 0, 7 ] , [ 55, 46, 34, 11 ] Name Index con len c2 c3 SL(2,Z/78Z) Matrix Generators 84 2 14 12 6 [ 1, 26, 26, 53 ] , [ 1, 39, 39, 40 ] , [ 7, 6, 10, 31 ] , [ 13, 42, 30, 67 ] , [ 25, 0, 0, 25 ] , [ 27, 26, 52, 27 ] , [ 53, 0, 0, 53 ] , [ 55, 6, 33, 49 ]

Chris Cummins and Sebastian Pauli, computed with MAGMA