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math.NT2023
A Database of Modular Forms on Noncongruence Subgroups
David Berghaus, Hartmut Monien, Danylo Radchenko
We present a database of several hundred modular forms up to and including weight six on noncongruence subgroups of index . In addition, our database contains expressions…
math.NT2022
On the computation of modular forms on noncongruence subgroups
David Berghaus, Hartmut Monien, Danylo Radchenko
We present two approaches that can be used to compute modular forms on noncongruence subgroups. The first approach uses Hejhal's method for which we improve the arbitrary precision…
math.NT2021
On Dirichlet eigenvalues of regular polygons
David Berghaus, Bogdan Georgiev, Hartmut Monien +1
We prove that the first Dirichlet eigenvalue of a regular -gon of area has an asymptotic expansion of the form as , where $λ_…