Exploring modular forms and the cohomology of local systems on moduli spaces by counting points

TL;DR

This paper investigates the relationship between modular forms and the cohomology of local systems on moduli spaces by using point counting over finite fields to gather experimental mathematical data.

Contribution

It introduces a novel experimental approach to studying modular forms through counting points on curves over finite fields, linking arithmetic geometry with modular form theory.

Findings

New data on modular forms obtained via point counting

Insights into the cohomology of local systems on moduli spaces

Enhanced understanding of the connection between arithmetic geometry and modular forms

Abstract

This is a report on a joint project in experimental mathematics with Jonas Bergstr\"om and Carel Faber where we obtain information about modular forms by counting curves over finite fields.