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 $\Gamma$.

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- Last edited by Bjorn Poonen on 2022-03-25 00:14:27

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