Congruence subgroup (reviewed)

A congruence subgroup $\Gamma$ of $\SL_2(\Z)$ is a subgroup that contains a principal congruence subgroup $\Gamma(N) := \ker \left( \operatorname{SL}_2(\mathbb{Z}) \to \operatorname{SL}_2(\mathbb{Z}/N\mathbb{Z}) \right)$ for some $N\ge 1$. The least such $N$ is the level of $\Gamma$.