A computation of modular forms of weight one and small level

TL;DR

This paper presents a computational study of weight one holomorphic cuspidal modular forms of small level, classifying them by their associated Artin representations and providing extensive data in accessible formats.

Contribution

It introduces new computational methods for weight one modular forms and offers a detailed classification and dataset of these forms up to level 1500.

Findings

Classification of modular forms by Artin image

Extensive dataset of Fourier expansions and forms

Novel computational techniques for weight one forms

Abstract

We report on a computation of holomorphic cuspidal modular forms of weight one and small level (currently level at most $1500$) and classification of them according to the projective image of their attached Artin representations. The data we have gathered, such as Fourier expansions and projective images of Hecke newforms and dimensions of space of forms, is available in both Magma and \texttt{Sage} readable formats on a webpage created in support of this ongoing project. We explain some of the novel aspects of these computations and what they have uncovered.