Experimental evidence for Maeda's conjecture on modular forms

Alexandru Ghitza, Angus McAndrew

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 14 000, 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.

Tbilisi Mathematical Journal, Vol. 5(2) (2012), pp. 55-69.