Computing Genus 1 Jacobi Forms

TL;DR

This paper introduces an algorithm for computing Fourier expansions of vector valued modular forms, applies it to special divisors on orthogonal modular varieties, and explores Hecke operators for Jacobi forms.

Contribution

It presents a novel algorithm for Fourier expansion computation and defines new Hecke operators for Jacobi forms, improving efficiency and expanding analytical tools.

Findings

Successful computation of Fourier expansions for vector valued modular forms.

Explicit linear equivalences of special divisors on orthogonal modular varieties.

Development of memory-efficient algorithms using new Hecke operator families.

Abstract

We develop an algorithm to compute Fourier expansions of vector valued modular for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three families of Hecke operators for Jacobi forms, and analyze the induced action on vector valued modular forms. The newspaces attached to one of these families are used to give a more memory efficient version of our algorithm.