Computing weight one modular forms over $\C$ and $\Fpbar$

Abstract

We report on a systematic computation of weight one cuspidal eigenforms for the group ${\Gamma }_1(N)$ in characteristic zero and in characteristic $p>2$. Perhaps the most surprising result was the existence of a mod 199 weight~1 cusp form of level 82 which does not lift to characteristic zero.

18 pages; second version incorporates a suggestion of Frank Calegari which makes a certain computation much more efficient (see Remark 8)

Cited by in corpus (4)

• Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
• Hecke stability and weight 1 modular forms
• Cohomological vanishing on Siegel modular varieties and applications to lifting Siegel modular forms
• Topological modular forms with level structure