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Experimental evidence for Maeda’s conjecture on modular forms. (English) Zbl 1280.11023
Summary: The authors 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 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.
Reviewer: Reviewer (Berlin)

MSC:
 11F25 Hecke-Petersson operators, differential operators (one variable) 11F11 Holomorphic modular forms of integral weight 11-04 Software, source code, etc. for problems pertaining to number theory
Keywords:
modular forms; Hecke operators
Software:
FLINT; LinBox; OEIS; SageMath
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