Experimental evidence for Maeda's conjecture on modular forms

Abstract

We describe a computational approach to the verification of Maeda's conjecture for the Hecke operator $T_2$ on the space of cusp forms of level one. We provide experimental evidence for all weights less than 14000, 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.