A Database of Modular Forms on Noncongruence Subgroups

2023/01/05 by David Berghaus, Berghaus, David, H. Monien +3
Mathematics · #11F11 #11F30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2301.02135

openalex publication_date 2023/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a database of several hundred modular forms up to and including weight six on noncongruence subgroups of index ≤ 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.

Related

• On the computation of modular forms on noncongruence subgroups
• The sporadic group J2, Hauptmodul and Belyi map
• Experimental finding of modular forms for noncongruence subgroups
• The unbounded denominator conjecture for the noncongruence subgroups of index 7
• Finite index subgroups of the modular group and their modular forms