Upper bound on the number of systems of Hecke eigenvalues for Siegel modular forms (mod p)

A. Ghitza
We derive an explicit upper bound for the number of systems of Hecke eigenvalues coming from Siegel modular forms (mod $p$).

Let $n_0(N,k)$ be the number of initial Fourier coefficients necessary to distinguish newforms of level $N$ and even weight $k$. We produce extensive data to support our conjecture that if $N$ is a fixed squarefree positive integer and $k$ is large then $n_0(N,k)$ is the least prime that does not divide $N$.