Integral traces of weak Maass forms of genus zero odd prime level

TL;DR

This paper extends the integral trace lifts from level 1 to genus zero odd prime levels, demonstrating that these lifts preserve the integrality of Fourier coefficients in weak Maass forms.

Contribution

It generalizes the integral trace lift construction to genus zero odd prime levels, maintaining the Fourier coefficient integrality property.

Findings

Lifts preserve integrality of Fourier coefficients at new levels

Extension from level 1 to genus zero odd prime levels

Supports broader applications in modular form theory

Abstract

Duke and the second author defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half integral weight and level 4 and showed that these lifts preserve the integrality of Fourier coefficients. We show that the generalization of these lifts to modular forms of genus 0 odd prime level also preserves the integrality of Fourier coefficients.