Computing power series expansions of modular forms

TL;DR

This paper presents a numerical method for computing power series expansions of modular forms on cocompact Fuchsian groups, utilizing fundamental domain computation and linear algebra techniques.

Contribution

The paper introduces a novel numerical approach for power series expansion of modular forms on cocompact Fuchsian groups, combining geometric and algebraic methods.

Findings

Effective computation of power series expansions demonstrated.

Method applicable to various cocompact Fuchsian groups.

Potential for advancing numerical analysis in modular forms.

Abstract

We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.