A remark on dimensions of spaces of modular forms
Let \(k,N\in \mathbb{N},k\) even, \(N\) squarefree. Denote by \(S_k(N)\) the space of elliptic cusp forms of weight \(k\) on \(\Gamma_0(N)\). Let \(S^*_k(N)\) be its semi-simple part, i.e. the largest submodule of \(S_k(N)\) on which the algebra generated by the Hecke operators \(T_p\), \(p\) prime, acts semi-simply. The author derives an explicit formula for \(\dim S^*_k(N)\), which surprisingly does not involve the prime decomposition of \(N\). As a corollary he obtains \[ \dim S^*_{k+12} (N)=1 + \dim S^*_k(N) \quad \text{for} \quad (k,N) \neq(2,1). \]
scientific article; zbMATH DE number 937048