A Database of Modular Forms on Noncongruence Subgroups

TL;DR

This paper introduces a comprehensive database of modular forms on noncongruence subgroups, including Belyi maps, elliptic curve equations, and high-precision Eisenstein series, facilitating further research in this area.

Contribution

The paper provides the first extensive database of modular forms on noncongruence subgroups, including explicit formulas and high-precision numerical data.

Findings

Database includes several hundred modular forms up to weight six.

Contains explicit Belyi maps and elliptic curve equations for relevant subgroups.

Provides high-precision numerical approximations of Eisenstein series.

Abstract

We present a database of several hundred modular forms up to and including weight six on noncongruence subgroups of index $\leq 17$. In addition, our database contains expressions for the Belyi map for genus zero subgroups and equations of the corresponding elliptic curves for genus one subgroups and numerical approximations of noncongruence Eisenstein series to 1500 digits precision.