Dimensions of spaces of modular forms

Abstract

We prove a conjecture of Ross concerning the value distribution of $\dim S_2^{\mathrm{new}}(\hat{I}{“}_0(N))$ for $N\in \mathbb{N}$, as well as analogous results for general weight $k\in 2\mathbb{N}$ and the full and twist-minimal spaces $S_k(\hat{I}{“}_0(N))$, $S_k^{\min }(\hat{I}{“}_0(N))$.

9 pages