Principal congruence subgroup (source code)

= Principal congruence subgroup
{title2=$\Gamma(N)$}

The principal congruence subgroup of level $N$ is
$$
\Gamma(N)=\ker\left(SL_n(\mathbb Z)\longrightarrow SL_n(\mathbb Z/N\mathbb Z)\right).
$$
It has finite index because the target is finite.