Modular function
= Modular function
{wiki}
A modular function of weight $k$ for a subgroup $\Gamma\leq SL_2(\mathbb Z)$ is a meromorphic function on the <complex upper half-plane> that satisfies
$$
f(\gamma\tau)=(c\tau+d)^k f(\tau)
$$
for $\gamma=\begin{pmatrix}a&b\\c&d\end{pmatrix}\in\Gamma$ and is meromorphic at every cusp.