Congruence subgroup of level $N$ of $\Sp(2g,\Z)$ (awaiting review)

A subgroup of the integral symplectic group $\Sp(2g,\Z)$ is called a congruence subgroup of level $N$ if it contains the principal congruence subgroup $\Gamma(N)$.

Examples of such subgroups are:

• the principal congruence subgroup $\Gamma(N)$;
• the Hecke subgroup $\Gamma_0(N)$;
• the subgroup $\Gamma_1(N)$.