= Solution
The <Gamma 1 congruence subgroup> is
$$
\Gamma_1(N)=\left\{
\begin{pmatrix}a&b\\c&d\end{pmatrix}\in SL_2(\mathbb Z):
a\equiv d\equiv1\pmod N, c\equiv0\pmod N
\right\}.
$$
The space $M_k(\Gamma_1(N))$ consists of the <holomorphic functions> $f:\mathfrak h\to\mathbb C$ satisfying
$$
f(\gamma\tau)=(c\tau+d)^kf(\tau)
$$
for every $\gamma\in\Gamma_1(N)$ and which are <holomorphic at a cusp> for every cusp. Its subspace $S_k(\Gamma_1(N))$ consists of the forms that vanish at every cusp.
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