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The group $\Gamma_0(N)$ in degree $g$ is the subgroup of the integral symplectic group $\Sp(2g,\Z)$, defined by \[ \Gamma_0(N)=\left\{ \begin{pmatrix}a&b\\c&d\end{pmatrix}\in \Sp(2g,\Z) : c \equiv 0 \bmod N \right\}. \] The group $\Gamma_0(N)$ is sometimes called the Hecke congruence subgroup of level $N$.

For $g=1$, it is the subgroup $\Gamma_0(N)$ of $\SL(2,\Z)$.

Knowl status:
  • Review status: beta
  • Last edited by Fabien Cléry on 2021-05-06 12:59:19
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