Congruences for Hermitan modular forms of degree 2

We give two congruence properties of Hermitian modular forms of degree 2 over $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-3})$. The one is a congruence criterion for Hermitian modular forms which is generalization of Sturm's theorem. Another is the well-definedness of the $p$-adic weight for Hermitian modular forms.