= Solution
For an integer $k$ and a <congruence subgroup> $\Gamma\leq SL_2(\mathbb Z)$, the space $M_k(\Gamma)$ consists of <holomorphic function>[holomorphic functions] $f:\mathfrak h\to\mathbb C$ satisfying
$$
(f|_k\gamma)(\tau)=(c\tau+d)^{-k}f(\gamma\tau)=f(\tau)
$$
for every $\gamma=\begin{pmatrix}a&b\\c&d\end{pmatrix}\in\Gamma$, and which are <holomorphic at a cusp>[holomorphic at every cusp]. This is the space of <modular form>[modular forms] of weight $k$ and level $\Gamma$.
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