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This repository collects the code and data used in verifying Maeda's conjecture on modular forms for weights up to 12000, as presented in the paper Experimental evidence for Maeda's conjecture on modular forms by A. Ghitza and A. McAndrew.

The algorithm was implemented in Sage, an open-source mathematical software system based on the Python language and tying together a large number of mathematical libraries.

The data

The results of the computations are stored in the two directories data and data-consec. They are stored in text files, one for each weight that was tested. The directory data holds the results of running the randomized version of the algorithm (as described in our paper), while the directory data-consec holds the results of running the consecutive version of the algorithm (as described in the 1999 paper of Conrey and Farmer -- see our paper for a precise reference).

The format of the result files

Each result file starts with some metadata:

  • the weight of the space
  • the total time taken by the computation
  • the time taken to compute the Victor Miller basis
  • the time taken to compute the matrix of the Hecke operator T2
  • the time taken to find a prime of each type I, II, and III, and the corresponding number of necessary attempts
  • the version of Sage used in the computation
  • the machine used for the computation
  • the date/time when the computation ended

The actual results follow. For each of the types I, II, and II, a prime p of that type is given, together with the reduction modulo p of the characteristic polynomial of T2.

How to use the code

Coming up.

(We plan to clean the code up, add some examples/doctests, and some comments.)