Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms
A. Ghitza
J. Number Theory 106, no. 2 (2004), 345-384.
We show that the systems of Hecke eigenvalues given by Siegel modular forms (mod $p$) are the same as the ones given by algebraic modular forms (mod $p$) on a quaternionic unitary group.