2 problems

A scalar modular form is a holomorphic function on the upper half-plane transforming with a prescribed weight under a subgroup of $\operatorname{SL}_2(\mathbb{Z})$; its Fourier coe…

Let $\Gamma=SL_2(\mathbb{Z})$, let $G$ be a finite-index subgroup of $\Gamma$, and let $\mathcal{M}_k(G)$ denote the space of modular forms of weight $k$ for $G$. The congruence cl…