[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 0

Groups of Level: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 24 25 26 27 28 30 32 36 48

^ Level 1 > 1A0 ^ Level 2 > 2A0 Name Index con len c2 c3 SL(2,Z/1Z) Matrix Generators Γ 1 1 1 1 1 Name Index con len c2 c3 SL(2,Z/2Z) Matrix Generators Γ2 2 1 1 0 2 [ 1, 1, 1, 0 ] Γ0(2), Γ1(2) 3 1 3 1 0 [ 0, 1, 1, 0 ] Γ(2) 6 1 1 0 0 Name Index con len c2 c3 SL(2,Z/3Z) Matrix Generators Γ3 3 1 1 3 0 [ 0, 1, 2, 0 ] , [ 0, 2, 1, 0 ] , [ 1, 2, 2, 2 ] , [ 2, 0, 0, 2 ] Γ0(3), Γ1(3) 4 1 4 0 1 [ 0, 2, 1, 2 ] , [ 1, 2, 1, 0 ] , [ 2, 0, 0, 2 ] , [ 2, 1, 2, 0 ] 6 1 3 2 0 [ 2, 0, 0, 2 ] , [ 2, 1, 1, 1 ] Γ(3) 12 1 1 0 0 [ 2, 0, 0, 2 ] Name Index con len c2 c3 SL(2,Z/4Z) Matrix Generators 4 1 4 2 1 [ 0, 1, 3, 0 ] , [ 1, 1, 1, 2 ] , [ 3, 0, 0, 3 ] Γ0(4), Γ1(4) 6 1 3 0 0 [ 0, 1, 3, 2 ] , [ 1, 2, 2, 1 ] , [ 2, 1, 3, 0 ] , [ 3, 2, 2, 3 ] 6 1 3 2 0 [ 0, 1, 3, 0 ] , [ 1, 2, 2, 1 ] , [ 2, 1, 3, 2 ] , [ 3, 2, 2, 3 ] 8 1 4 0 2 [ 1, 1, 1, 2 ] , [ 3, 0, 0, 3 ] 12 1 3 0 0 [ 1, 2, 2, 1 ] , [ 3, 2, 2, 3 ] 12 1 6 2 0 [ 0, 1, 3, 0 ] , [ 3, 0, 0, 3 ] Γ(4) 24 1 1 0 0 [ 3, 0, 0, 3 ] Name Index con len c2 c3 SL(2,Z/5Z) Matrix Generators 5 1 5 1 2 [ 1, 1, 4, 0 ] , [ 2, 1, 0, 3 ] , [ 4, 0, 0, 4 ] , [ 4, 2, 4, 1 ] Γ0(5) 6 1 6 2 0 [ 2, 3, 3, 0 ] , [ 4, 0, 0, 4 ] , [ 4, 1, 3, 1 ] 10 1 10 2 1 [ 3, 0, 1, 2 ] , [ 4, 0, 0, 4 ] , [ 4, 3, 3, 0 ] Γ1(5) 12 1 6 0 0 [ 2, 3, 3, 0 ] , [ 4, 0, 0, 4 ] 15 1 5 3 0 [ 1, 3, 1, 4 ] , [ 3, 0, 3, 2 ] , [ 4, 0, 0, 4 ] 20 1 10 0 2 [ 4, 0, 0, 4 ] , [ 4, 3, 3, 0 ] 30 1 15 2 0 [ 2, 4, 0, 3 ] , [ 4, 0, 0, 4 ] Γ(5) 60 1 1 0 0 [ 4, 0, 0, 4 ] Name Index con len c2 c3 SL(2,Z/6Z) Matrix Generators 6 1 2 0 3 [ 0, 1, 5, 1 ] , [ 1, 2, 2, 5 ] , [ 3, 4, 2, 3 ] , [ 5, 0, 0, 5 ] , [ 5, 3, 1, 2 ] , [ 5, 4, 4, 1 ] 6 1 3 4 0 [ 2, 1, 1, 4 ] , [ 3, 2, 4, 3 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 1, 1 ] 8 1 4 0 2 [ 1, 3, 3, 4 ] , [ 3, 2, 4, 5 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 2, 3 ] 9 1 3 3 0 [ 3, 2, 4, 3 ] , [ 4, 3, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] 12 1 3 4 0 [ 1, 3, 3, 4 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 1, 1 ] Γ0(6), Γ1(6) 12 1 12 0 0 [ 1, 0, 3, 1 ] , [ 3, 2, 4, 5 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 2, 3 ] , [ 5, 4, 5, 3 ] 18 1 9 2 0 [ 4, 3, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] 18 1 9 4 0 [ 0, 1, 5, 0 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] 24 1 4 0 0 [ 3, 2, 4, 5 ] , [ 3, 4, 2, 1 ] , [ 5, 4, 2, 3 ] 24 1 8 0 3 [ 2, 1, 5, 3 ] , [ 5, 0, 0, 5 ] 36 1 3 0 0 [ 1, 0, 3, 1 ] , [ 5, 0, 0, 5 ] 36 1 9 4 0 [ 0, 1, 5, 0 ] , [ 0, 5, 1, 0 ] , [ 5, 0, 0, 5 ] Name Index con len c2 c3 SL(2,Z/7Z) Matrix Generators 7 2 7 3 1 [ 0, 3, 2, 0 ] , [ 2, 5, 6, 5 ] , [ 4, 0, 6, 2 ] , [ 6, 0, 0, 6 ] , [ 6, 6, 2, 1 ] Γ0(7) 8 1 8 0 2 [ 3, 2, 0, 5 ] , [ 5, 3, 4, 4 ] , [ 6, 0, 0, 6 ] 14 2 7 2 2 [ 1, 3, 4, 6 ] , [ 2, 0, 1, 4 ] , [ 2, 5, 6, 5 ] , [ 6, 0, 0, 6 ] 21 1 21 5 0 [ 0, 3, 2, 0 ] , [ 1, 3, 4, 6 ] , [ 2, 5, 6, 5 ] , [ 6, 0, 0, 6 ] Γ1(7) 24 1 8 0 0 [ 6, 0, 0, 6 ] , [ 6, 2, 5, 3 ] 28 1 28 4 1 [ 0, 3, 2, 0 ] , [ 4, 3, 5, 4 ] , [ 6, 0, 0, 6 ] 42 2 7 6 0 [ 0, 3, 2, 0 ] , [ 2, 5, 6, 5 ] , [ 6, 0, 0, 6 ] Name Index con len c2 c3 SL(2,Z/8Z) Matrix Generators 8 2 4 2 2 [ 1, 4, 4, 1 ] , [ 4, 1, 7, 0 ] , [ 4, 3, 5, 4 ] , [ 5, 0, 4, 5 ] , [ 5, 4, 0, 5 ] , [ 6, 3, 7, 1 ] , [ 7, 0, 0, 7 ] 12 1 3 4 0 [ 0, 5, 3, 0 ] , [ 3, 6, 6, 7 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 5 ] , [ 7, 4, 4, 7 ] , [ 7, 6, 6, 3 ] Γ0(8) 12 1 6 0 0 [ 1, 4, 4, 1 ] , [ 3, 0, 0, 3 ] , [ 4, 5, 3, 2 ] , [ 5, 4, 4, 5 ] , [ 7, 2, 6, 3 ] 12 1 6 2 0 [ 0, 5, 3, 0 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 5 ] , [ 7, 4, 4, 7 ] , [ 7, 6, 2, 3 ] 16 1 4 0 4 [ 1, 1, 5, 6 ] , [ 1, 4, 4, 1 ] , [ 5, 0, 4, 5 ] , [ 6, 3, 7, 1 ] , [ 7, 0, 0, 7 ] 16 1 16 4 1 [ 0, 1, 7, 0 ] , [ 0, 3, 5, 0 ] , [ 2, 3, 3, 5 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] 24 1 3 0 0 [ 1, 2, 0, 1 ] , [ 1, 4, 0, 1 ] , [ 1, 6, 0, 1 ] , [ 3, 2, 0, 3 ] , [ 5, 4, 0, 5 ] 24 1 6 4 0 [ 0, 5, 3, 0 ] , [ 1, 4, 4, 1 ] , [ 5, 0, 0, 5 ] , [ 7, 4, 4, 7 ] Γ1(8) 24 1 12 0 0 [ 3, 2, 6, 7 ] , [ 4, 5, 3, 2 ] , [ 5, 4, 4, 5 ] , [ 5, 6, 2, 1 ] 24 1 12 0 0 [ 1, 2, 4, 1 ] , [ 1, 4, 0, 1 ] , [ 1, 6, 4, 1 ] , [ 3, 2, 0, 3 ] , [ 5, 4, 4, 5 ] 24 1 12 2 0 [ 0, 5, 3, 0 ] , [ 1, 0, 4, 1 ] , [ 1, 4, 4, 1 ] , [ 7, 4, 4, 7 ] 24 1 12 4 0 [ 0, 7, 1, 0 ] , [ 3, 6, 6, 7 ] , [ 5, 4, 4, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 2, 2, 3 ] 32 2 16 4 2 [ 0, 1, 7, 0 ] , [ 2, 3, 3, 5 ] , [ 7, 0, 0, 7 ] 48 1 3 0 0 [ 1, 0, 4, 1 ] , [ 1, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 4, 4, 7 ] 48 1 6 0 0 [ 1, 4, 0, 1 ] , [ 5, 6, 0, 5 ] , [ 7, 4, 0, 7 ] 48 1 12 4 0 [ 0, 7, 1, 0 ] , [ 5, 4, 4, 5 ] , [ 7, 0, 0, 7 ] Name Index con len c2 c3 SL(2,Z/9Z) Matrix Generators 9 1 9 5 0 [ 0, 1, 8, 0 ] , [ 1, 7, 1, 8 ] , [ 2, 6, 6, 5 ] , [ 7, 0, 0, 4 ] , [ 7, 6, 6, 4 ] Γ0(9) 12 1 4 0 0 [ 4, 0, 6, 7 ] , [ 7, 0, 6, 4 ] , [ 7, 0, 8, 4 ] , [ 8, 0, 0, 8 ] 12 1 4 0 3 [ 1, 3, 2, 7 ] , [ 4, 0, 6, 7 ] , [ 7, 0, 6, 4 ] , [ 8, 0, 0, 8 ] 18 1 3 6 0 [ 0, 1, 8, 0 ] , [ 4, 6, 6, 7 ] , [ 5, 3, 3, 2 ] , [ 7, 0, 0, 4 ] 18 1 18 2 0 [ 0, 1, 8, 0 ] , [ 4, 6, 3, 7 ] , [ 7, 0, 0, 4 ] , [ 8, 0, 0, 8 ] 27 1 27 3 3 [ 0, 1, 8, 0 ] , [ 0, 8, 1, 0 ] , [ 1, 3, 2, 7 ] , [ 4, 1, 1, 5 ] , [ 8, 0, 0, 8 ] 27 1 27 7 0 [ 0, 1, 8, 0 ] , [ 1, 7, 1, 8 ] , [ 4, 6, 6, 7 ] , [ 5, 3, 3, 2 ] 36 1 6 0 0 [ 4, 0, 0, 7 ] , [ 4, 3, 6, 7 ] , [ 8, 0, 0, 8 ] Γ1(9) 36 1 12 0 0 [ 1, 0, 6, 1 ] , [ 7, 0, 5, 4 ] , [ 8, 0, 0, 8 ] 36 1 12 0 3 [ 1, 0, 6, 1 ] , [ 1, 3, 2, 7 ] , [ 8, 0, 0, 8 ] Name Index con len c2 c3 SL(2,Z/10Z) Matrix Generators 10 1 5 0 4 [ 1, 4, 8, 3 ] , [ 1, 5, 5, 6 ] , [ 1, 8, 6, 9 ] , [ 3, 0, 8, 7 ] , [ 9, 0, 0, 9 ] 12 1 6 4 0 [ 6, 5, 5, 1 ] , [ 7, 8, 8, 5 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 3, 1 ] Γ0(10) 18 1 18 2 0 [ 1, 0, 5, 1 ] , [ 7, 8, 8, 5 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 3, 1 ] 20 1 10 4 2 [ 1, 5, 5, 6 ] , [ 7, 4, 5, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] 30 1 10 0 6 [ 7, 6, 0, 3 ] , [ 8, 1, 7, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 2, 4, 1 ] Γ1(10) 36 1 18 0 0 [ 5, 2, 2, 7 ] , [ 5, 2, 7, 7 ] , [ 9, 0, 0, 9 ] 36 1 18 4 0 [ 1, 4, 7, 9 ] , [ 5, 2, 2, 7 ] , [ 9, 0, 0, 9 ] Name Index con len c2 c3 SL(2,Z/11Z) Matrix Generators 11 2 11 3 2 [ 8, 2, 6, 3 ] , [ 9, 4, 2, 1 ] , [ 10, 0, 0, 10 ] Name Index con len c2 c3 SL(2,Z/12Z) Matrix Generators 12 1 4 6 0 [ 1, 4, 4, 5 ] , [ 1, 9, 9, 10 ] , [ 4, 9, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 9, 8, 4, 9 ] 16 1 4 0 4 [ 1, 6, 6, 1 ] , [ 3, 8, 10, 11 ] , [ 4, 3, 9, 7 ] , [ 7, 0, 6, 7 ] , [ 8, 1, 11, 3 ] , [ 9, 8, 4, 5 ] , [ 11, 0, 0, 11 ] 18 1 3 6 0 [ 1, 4, 4, 5 ] , [ 1, 6, 6, 1 ] , [ 4, 3, 9, 4 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 9, 4, 8, 9 ] 18 1 9 4 0 [ 1, 6, 6, 1 ] , [ 4, 3, 9, 10 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 9, 4, 2, 9 ] , [ 10, 3, 9, 4 ] Γ0(12) 24 1 12 0 0 [ 1, 0, 6, 1 ] , [ 7, 0, 6, 7 ] , [ 9, 4, 8, 1 ] , [ 9, 8, 1, 5 ] , [ 9, 8, 4, 5 ] , [ 11, 4, 5, 3 ] , [ 11, 4, 8, 3 ] 24 1 12 8 0 [ 0, 1, 11, 0 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 8, 1 ] , [ 7, 0, 0, 7 ] , [ 8, 1, 7, 4 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 0, 11 ] 36 1 9 4 0 [ 1, 6, 6, 1 ] , [ 1, 10, 4, 5 ] , [ 4, 9, 3, 10 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 2, 1 ] , [ 7, 0, 0, 7 ] 36 1 9 8 0 [ 0, 1, 11, 0 ] , [ 1, 6, 6, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 6, 6, 7 ] , [ 8, 11, 5, 4 ] , [ 11, 0, 0, 11 ] , [ 11, 4, 4, 7 ] 48 1 12 0 0 [ 1, 6, 0, 1 ] , [ 3, 4, 8, 7 ] , [ 5, 4, 8, 9 ] , [ 7, 6, 6, 7 ] , [ 9, 8, 4, 5 ] Γ1(12) 48 1 24 0 0 [ 3, 4, 8, 7 ] , [ 5, 4, 2, 9 ] , [ 5, 4, 5, 9 ] , [ 9, 8, 1, 5 ] , [ 9, 8, 4, 5 ] Name Index con len c2 c3 SL(2,Z/13Z) Matrix Generators Γ0(13) 14 1 14 2 2 [ 1, 3, 11, 8 ] , [ 7, 7, 4, 6 ] , [ 9, 2, 7, 6 ] , [ 12, 0, 0, 12 ] 28 1 14 0 4 [ 0, 3, 4, 2 ] , [ 4, 0, 11, 10 ] , [ 5, 7, 3, 7 ] 42 1 14 6 0 [ 0, 3, 4, 2 ] , [ 6, 6, 9, 7 ] , [ 7, 2, 7, 4 ] Name Index con len c2 c3 SL(2,Z/14Z) Matrix Generators 14 2 7 4 2 [ 1, 9, 4, 9 ] , [ 5, 8, 2, 9 ] , [ 7, 12, 4, 7 ] , [ 8, 7, 7, 1 ] , [ 11, 12, 0, 9 ] , [ 13, 0, 0, 13 ] 16 1 8 0 4 [ 1, 7, 7, 8 ] , [ 11, 8, 12, 5 ] , [ 13, 10, 2, 7 ] , [ 13, 12, 12, 9 ] 48 1 16 0 6 [ 0, 1, 13, 13 ] , [ 3, 10, 8, 13 ] , [ 11, 8, 12, 5 ] , [ 13, 0, 0, 13 ] Name Index con len c2 c3 SL(2,Z/15Z) Matrix Generators 15 2 5 3 3 [ 1, 3, 6, 4 ] , [ 1, 9, 8, 13 ] , [ 4, 0, 0, 4 ] , [ 6, 10, 5, 6 ] , [ 11, 0, 0, 11 ] , [ 11, 5, 5, 1 ] , [ 13, 0, 3, 7 ] 18 1 6 6 0 [ 6, 10, 5, 6 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 0, 11 ] , [ 11, 5, 5, 1 ] , [ 14, 0, 0, 14 ] , [ 14, 1, 13, 1 ] 36 1 18 8 0 [ 2, 10, 7, 13 ] , [ 6, 10, 5, 6 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 0, 11 ] , [ 14, 0, 0, 14 ] Name Index con len c2 c3 SL(2,Z/16Z) Matrix Generators 16 2 8 2 4 [ 1, 8, 8, 1 ] , [ 1, 9, 5, 14 ] , [ 1, 12, 4, 1 ] , [ 4, 5, 3, 4 ] , [ 9, 0, 8, 9 ] , [ 13, 0, 12, 5 ] , [ 14, 11, 7, 1 ] , [ 15, 8, 8, 15 ] 24 1 3 8 0 [ 1, 8, 8, 1 ] , [ 1, 10, 10, 5 ] , [ 2, 7, 13, 14 ] , [ 5, 4, 4, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 6, 6, 15 ] , [ 15, 0, 0, 15 ] , [ 15, 12, 12, 15 ] Γ0(16) 24 1 6 0 0 [ 1, 8, 8, 1 ] , [ 1, 12, 12, 1 ] , [ 5, 4, 12, 13 ] , [ 6, 1, 7, 12 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 2, 14, 7 ] , [ 13, 2, 6, 1 ] 24 1 12 0 0 [ 1, 8, 8, 1 ] , [ 1, 12, 4, 1 ] , [ 2, 9, 7, 0 ] , [ 5, 4, 12, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 2, 14, 7 ] , [ 13, 2, 14, 1 ] 24 1 12 2 0 [ 1, 8, 8, 1 ] , [ 4, 3, 5, 4 ] , [ 9, 0, 0, 9 ] , [ 11, 6, 10, 7 ] , [ 13, 8, 8, 5 ] , [ 13, 12, 4, 5 ] , [ 15, 8, 8, 15 ] 32 1 4 0 8 [ 1, 8, 8, 1 ] , [ 7, 0, 8, 7 ] , [ 9, 0, 8, 9 ] , [ 9, 1, 5, 6 ] , [ 9, 4, 4, 9 ] , [ 13, 0, 12, 5 ] , [ 13, 8, 4, 5 ] , [ 15, 8, 8, 15 ] 48 1 3 0 0 [ 1, 4, 0, 1 ] , [ 1, 6, 0, 1 ] , [ 1, 8, 0, 1 ] , [ 3, 12, 8, 11 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 0, 9 ] , [ 13, 0, 8, 5 ] 48 1 12 0 0 [ 1, 8, 8, 1 ] , [ 2, 1, 15, 0 ] , [ 9, 8, 8, 9 ] , [ 13, 4, 12, 5 ] , [ 13, 6, 10, 1 ] , [ 13, 12, 4, 5 ] , [ 15, 6, 10, 3 ] Name Index con len c2 c3 SL(2,Z/18Z) Matrix Generators 18 2 9 8 0 [ 1, 9, 9, 10 ] , [ 5, 12, 12, 11 ] , [ 7, 0, 0, 13 ] , [ 9, 10, 17, 9 ] , [ 11, 10, 1, 1 ] , [ 13, 6, 6, 7 ] 24 1 4 0 6 [ 1, 0, 6, 1 ] , [ 1, 9, 9, 10 ] , [ 1, 12, 2, 7 ] , [ 13, 0, 12, 7 ] , [ 17, 0, 0, 17 ] 24 1 8 0 3 [ 1, 0, 6, 1 ] , [ 1, 0, 10, 1 ] , [ 7, 15, 3, 4 ] , [ 13, 0, 12, 7 ] , [ 17, 0, 0, 17 ] 36 1 3 12 0 [ 5, 12, 12, 11 ] , [ 7, 0, 0, 13 ] , [ 7, 12, 12, 13 ] , [ 9, 10, 17, 9 ] , [ 10, 9, 9, 1 ] Γ0(18) 36 1 12 0 0 [ 1, 0, 6, 1 ] , [ 1, 0, 9, 1 ] , [ 1, 0, 12, 1 ] , [ 7, 0, 14, 13 ] , [ 13, 0, 0, 7 ] , [ 17, 0, 0, 17 ] Name Index con len c2 c3 SL(2,Z/20Z) Matrix Generators 36 1 18 4 0 [ 1, 0, 10, 1 ] , [ 5, 12, 12, 17 ] , [ 5, 12, 17, 17 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 10, 11 ] , [ 11, 14, 17, 9 ] Name Index con len c2 c3 SL(2,Z/21Z) Matrix Generators 21 2 7 9 0 [ 1, 7, 7, 8 ] , [ 1, 18, 3, 13 ] , [ 6, 17, 4, 15 ] , [ 7, 3, 9, 7 ] , [ 7, 15, 6, 13 ] , [ 8, 0, 0, 8 ] , [ 10, 15, 18, 4 ] , [ 13, 0, 0, 13 ] , [ 15, 7, 14, 15 ] Name Index con len c2 c3 SL(2,Z/24Z) Matrix Generators 36 1 3 12 0 [ 1, 0, 12, 1 ] , [ 1, 8, 20, 17 ] , [ 1, 16, 4, 17 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 12, 13 ] , [ 13, 12, 6, 13 ] , [ 13, 12, 18, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 18, 3, 13 ] 48 1 12 0 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 8, 0, 1 ] , [ 7, 12, 6, 7 ] , [ 11, 0, 21, 11 ] , [ 13, 0, 0, 13 ] , [ 13, 0, 12, 13 ] , [ 19, 12, 15, 7 ] , [ 23, 0, 0, 23 ] Name Index con len c2 c3 SL(2,Z/25Z) Matrix Generators Γ0(25) 30 1 30 2 0 [ 6, 10, 20, 21 ] , [ 8, 21, 6, 19 ] , [ 9, 11, 18, 11 ] , [ 11, 0, 10, 16 ] , [ 24, 0, 0, 24 ] 60 1 6 0 0 [ 6, 0, 5, 21 ] , [ 6, 15, 15, 21 ] , [ 7, 23, 18, 20 ] , [ 16, 0, 15, 11 ] , [ 19, 0, 20, 4 ] Name Index con len c2 c3 SL(2,Z/26Z) Matrix Generators 28 1 14 4 4 [ 5, 20, 16, 7 ] , [ 11, 14, 3, 11 ] , [ 13, 16, 4, 15 ] , [ 14, 13, 13, 1 ] , [ 17, 0, 24, 23 ] 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 ] , [ 16, 18, 25, 13 ] , [ 26, 0, 0, 26 ] Name Index con len c2 c3 SL(2,Z/28Z) Matrix Generators 32 1 8 0 8 [ 1, 14, 14, 1 ] , [ 13, 14, 0, 13 ] , [ 13, 20, 8, 21 ] , [ 15, 14, 0, 15 ] , [ 17, 24, 8, 13 ] , [ 22, 21, 21, 1 ] , [ 25, 8, 12, 5 ] Name Index con len c2 c3 SL(2,Z/30Z) Matrix Generators 36 1 6 12 0 [ 1, 10, 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 ] 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 ] , [ 19, 26, 22, 15 ] , [ 23, 10, 30, 27 ] , [ 26, 29, 27, 8 ] Name Index con len c2 c3 SL(2,Z/36Z) Matrix Generators 48 1 4 0 12 [ 1, 0, 24, 1 ] , [ 1, 18, 18, 1 ] , [ 10, 27, 27, 1 ] , [ 19, 18, 0, 19 ] , [ 25, 0, 24, 13 ] , [ 25, 24, 16, 1 ] , [ 35, 0, 0, 35 ] Name Index con len c2 c3 SL(2,Z/48Z) Matrix Generators 72 1 3 24 0 [ 1, 0, 24, 1 ] , [ 3, 10, 47, 45 ] , [ 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 ] , [ 41, 24, 36, 41 ]

Chris Cummins and Sebastian Pauli, computed with MAGMA