SL2/Z/Kongruenzuntergruppe/1/Definition

Zu  ${}N\in \mathbb {N}$  setzt man

$\Gamma _{1}(N)=\left\{M={\begin{pmatrix}a&b\\c&d\end{pmatrix}}\in \Gamma _{0}(N)\mid a=1\mod N\right\}=\left\{M={\begin{pmatrix}a&b\\c&d\end{pmatrix}}\in \operatorname {SL} _{2}\!{\left(\mathbb {Z} \right)}\mid a=d=1\mod N,\,c=0\mod N\right\}\subseteq \operatorname {SL} _{2}\!{\left(\mathbb {Z} \right)}\,.$