Multiplicities of representations in spaces of modular forms

BinYong Hsie

This paper shows that for a given irreducible representation $\rho$ of $\Gamma /{\Gamma }_1$, the two functions dim($M_k({\Gamma }_1,\rho )$) and dim($S_k({\Gamma }_1,\rho )$) of $k$ are almost linear functions.