Congruences for Hermitan modular forms of degree 2

TL;DR

This paper establishes new congruence criteria for Hermitian modular forms of degree 2 over specific imaginary quadratic fields, extending Sturm's theorem and defining p-adic weights for these forms.

Contribution

It introduces a generalized congruence criterion for Hermitian modular forms and defines the concept of p-adic weight in this context.

Findings

A congruence criterion generalizing Sturm's theorem for Hermitian modular forms.

Proof of the well-definedness of p-adic weights for these forms.

Application of results to specific imaginary quadratic fields.

Abstract

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.