Computing Jacobi Forms
Nathan C. Ryan, Nicol\'as Sirolli, Nils-Peter Skoruppa and, Gonzalo Tornar\'ia

TL;DR
This paper presents an implementation for computing Jacobi forms using modular symbols, enabling efficient calculation of Jacobi eigenforms of large index and providing several illustrative examples.
Contribution
The authors develop a novel method to compute Jacobi forms directly from modular eigensymbols, improving efficiency for large index cases.
Findings
Successfully computed Jacobi eigenforms of large index
Demonstrated the method with multiple examples
Enabled direct generation of Jacobi forms from modular symbols
Abstract
We describe an implementation for computing holomorphic and skew-holomorphic Jacobi forms of integral weight and scalar index on the full modular group. This implementation is based on formulas derived by one of the authors which express Jacobi forms in terms of modular symbols of elliptic modular forms. Since this method allows to generate a Jacobi eigenform directly from a given modular eigensymbol without reference to the whole ambient space of Jacobi forms it makes it possible to compute Jacobi Hecke eigenforms of large index. We illustrate our method with several examples.
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