Spaces of modular forms (mathlib) (awaiting review)

This is ModularForm $\Gamma$ $k$ in mathlib. The LMFDB definition is specified by a level $N$, weight $k$, and character $\chi$, whereas the mathlib definition is specified by a subgroup $\Gamma$ and weight $k$, with no character.

For $\Gamma=\Gamma_0(N)$, the mathlib space corresponds to $M_k(N,1)$, the space of modular forms with trivial character.

For $\Gamma=\Gamma_1(N)$, recall the decomposition $M_k(\Gamma_1(N))=\bigoplus_{\chi\bmod N} M_k(N,\chi)$ where only characters satisfying $\chi(-1)=(-1)^k$ can contribute to nonzero summands. Hence the mathlib space for $M_k(\Gamma_1(N))$ is the direct sum of the corresponding character spaces from the LMFDB.