On $p$-adic Siegel modular forms of non-real Nebentypus of degree 2

TL;DR

This paper proves that all Siegel modular forms with non-real Nebentypus for a specific subgroup are $p$-adic, utilizing a Maass lift, expanding understanding of their $p$-adic properties.

Contribution

It establishes that non-real Nebentypus Siegel modular forms of degree 2 are $p$-adic, using a Maass lift, which was not previously known.

Findings

All such forms are $p$-adic.

Uses Maass lift to establish $p$-adic property.

Extends the theory of $p$-adic Siegel modular forms.

Abstract

We show that all Siegel modular forms of non-real Nebentypus for $\Gamma_0^{(2)}(p)$ are $p$-adic Siegel modular forms by using a Maass lift.