Memorandum on Dimension Formulas for Spaces of Jacobi Forms

TL;DR

This paper provides explicit formulas for calculating the dimensions of spaces of Jacobi cusp forms with integral weight and index on subgroups of SL, facilitating easier analysis of these mathematical objects.

Contribution

It presents ready-to-use dimension formulas for Jacobi cusp forms of integral weight and index on subgroups of SL, advancing computational methods in this area.

Findings

Explicit dimension formulas for Jacobi cusp forms

Simplified computation of Jacobi form spaces

Applicable to subgroups of SL

Abstract

We state ready to compute dimension formulas for the spaces of Jacobi cusp forms of integral weight $k$ and integral scalar index $m$ on subgroups of $\SL$.