  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 Klingen-Eisenstein
series and cusp forms, which can be regarded as a generalization of Ramanujan's
congruence. We will conclude by giving numerical examples.
