On Siegel modular forms of level p and their properties mod p

Abstract

Using theta series we construct Siegel modular forms of level p which behave well modulo p in all cusps. This construction allows us to show (under a mild condition) that all Siegel modular forms of level p and weight 2 are congruent mod p to level one modular forms of weight p + 1; in particular, this is true for Yoshidal lifts of level p.