Group $\Gamma_0(N)$, subgroup of $\mathrm{Sp}(2g,\mathbb Z)$ (awaiting review)

The group $\Gamma_0(N)$ in degree $g$ is a subgroup of the integral symplectic group $\operatorname{Sp}(2g,{\Bbb Z})$, defined by $$\Gamma_0(N)=\left\{ \begin{pmatrix}A&B\\C&D\end{pmatrix}\in \operatorname{Sp}(2g,{\Bbb Z}) : C \equiv 0 \pmod N \right\}.$$