Fourier coefficients for twists of Siegel paramodular forms (expanded version)

TL;DR

This paper derives formulas for Fourier coefficients of twisted Siegel paramodular forms, enabling nonvanishing verification and showing that twists of Maass forms are zero, advancing understanding of modular form twists.

Contribution

It provides explicit formulas for Fourier coefficients of paramodular twists of Siegel forms, a novel computational tool in the field.

Findings

Formulas for Fourier coefficients of twisted Siegel forms

Verification method for nonvanishing of twists

Proof that twists of Maass forms are zero

Abstract

In this paper, we calculate the Fourier coefficients of the paramodular twist of a Siegel modular form of paramodular level $N$ by a nontrivial quadratic Dirichlet character mod $p$ for $p$ a prime not dividing $N$. As an application, these formulas can be used to verify the nonvanishing of the twist for particular examples. We also deduce that the twists of Maass forms are identically zero.