Upper bound on the number of systems of hecke eigenvalues for siegel modular forms (modp)

Abstract

We derive an explicit upper bound for the number N(g,N,p) of systems of Hecke eigenvalues coming from Siegel modular forms mod p) of dimension g and level N relatively prime to p. In the special case of elliptic modular forms (g=1), our result agrees with recent work of G. Herrick.