Congruence Subgroups of PSL(2,Z)
PSL(2,Z) acts on the extended upper half plane H by fractional linear transformations, and the genus of a subgroup U is the genus of the corresponding surface H/U. The principal congruence subgroup Gamma(N) of level N is the kernel of reduction modulo N, and a congruence subgroup is one containing Gamma(N) for some N. This database contains all congruence subgroups of genus up to 24.