Note on mod p property of Hermitian modular forms

Abstract

The mod $p$ kernel of the theta operator is the set of modular forms whose image of the theta operator is congruent to zero modulo a prime $p$. In the case of Siegel modular forms, the authors found interesting examples of such modular forms. For example, Igusa's odd weight cusp form is an element of mod 23 kernel of the theta operator. In this paper, we give some examples which represent elements in the mod $p$ kernel of the theta operator in the case of Hermitian modular forms of degree 2.