Experimental evidence for Maeda's conjecture on modular forms

TL;DR

This paper presents a computational method to verify Maeda's conjecture for the Hecke operator T2 on level one cusp forms, providing extensive experimental evidence up to weight 12000 using Sage software.

Contribution

It introduces a new computational approach and provides extensive empirical verification of Maeda's conjecture for high weights, with openly available code and data.

Findings

Confirmed Maeda's conjecture for weights less than 12000

Developed an efficient Sage-based algorithm for verification

Published accessible data and code for further research

Abstract

We describe a computational approach to the verification of Maeda's conjecture for the Hecke operator T2 on the space of cusp forms of level one. We provide experimental evidence for all weights less than 12000, as well as some applications of these results. The algorithm was implemented using the mathematical software Sage, and the code and resulting data were made freely available.