Subgroup $\Gamma_1(N)$ of $\Sp(2g,\Z)$ (awaiting review)

The subgroup $\Gamma_1(N)$ of the integral symplectic group $\Sp(2g,\Z)$ is defined by: \[ \Gamma_1(N)= \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix}\in \Sp(2g,\Z)\ \vert \begin{pmatrix} a & b \\ c & d \end{pmatrix}\equiv \begin{pmatrix} 1_g & * \\ 0 & 1_g \end{pmatrix} \bmod N \right\}. \] For $g=1$, it is the subgroup $\Gamma_1(N)$ of $\SL(2,\Z)$.