Let $K$ be an imaginary quadratic field with ring of integers $\mathcal{O}_K$. For a nonzero ideal $\mathfrak{N}$ of $\mathcal{O}_K$, the **principal congruence subgroup of level $\mathfrak{N}$** is
$$\Gamma(\mathfrak{N}) = \{\gamma \in \textrm{PSL}_2(\mathcal{O}_K) : \gamma\equiv \pm 1 \!\! \pmod{\mathfrak{N}} \}.$$ A subgroup of $\textrm{PSL}_2(\mathcal{O}_K)$ is called a **congruence subgroup** if it contains a principal congruence subgroup.

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- Last edited by John Voight on 2019-04-30 23:40:20

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