Experimental evidence for Maeda's conjecture on modular forms
  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. 
Alexandru Ghitza and Angus McAndrew
math.NT