Ramanujan type congruences for the Klingen-Eisenstein series

In the case of Siegel modular forms of degree n, we prove that, for almost all prime ideals \frak{p} in any ring of algebraic integers, mod \frak{p}^m cusp forms are congruent to true cusp forms of the same weight. As an application of this property, we give congruences for the... Show more