I would guess that the following is very well known, but I don't know the answer and I couldn't find anything with some googling.
Let $\Gamma \subset \mathrm{SL}(2,\mathbf Z)$ be a congruence subgroup, I would be happy with an answer just for $\Gamma(n)$ or $\Gamma_0(n)$. Denote $S_k(\Gamma)$ the space of weight $k$ cusp forms for $\Gamma$ and $S_k^{\mathrm{CM}}(\Gamma) \subset S_k(\Gamma)$ the subspace generated by all cusp forms with complex multiplication. Dimension formulas for the spaces $S_k(\Gamma)$ are well known, but what is the dimension of $S_k^{\mathrm{CM}}(\Gamma)$?
