Data and Code

Here is a selected collection of data and code related to some of my projects. Feel free to contact me with questions, and/or requests for additional data/code.

Galois orbits in weight 2 with prime level

The following data tells you the size of every Galois orbit in S₂(N) (S₂(Γ₀(N)) for N < 60000 prime.

text file - each line is of the form N: d₁, d₂, ..., d_r where N is a prime level, and the d_i's are sizes of the Galois orbits
sage object file - this is a saved dictionary in sage (version 8.7); the keys are the levels N, and the associated values are lists of the sizes of the Galois orbits

This data was generated in Sage using the OU Supercomputing Center (OSCER) for my paper:

An on-average Maeda-type conjecture in the level aspect
Proceedings of the AMS, Vol. 149, No. 4 (2021), 1373-1386

This paper explains how this data was generated.

Dimensions of modular forms

Here is code to compute dimensions of newspaces of (elliptic) modular forms of squarefree level, as well as the dimensions of individual Atkin-Lehner eigenspaces.

sage 8 code (python 2 syntax)
sage 9 code (python 3 syntax)

The full newspace dimension is given in a formula by Greg Martin (JNT, 2005), and the Atkin-Lehner eigenspace dimensions are given in my paper:

Refined dimensions of cusp forms, and equidistribution and bias of signs preprint version]
Journal of Number Theory, Vol. 188 (2018), 1-17.

Quaternionic modular forms code

Here is some code to compute examples of definite quaternionic modular eigenforms of trivial weight and character, which are the subject of a number of my papers from 2017-2020+, especially papers 20, 23 and 26 listed on my math page. The nonconstant eigenforms here correspond the newforms of weight 2 and squarefree levels N (with an odd number of prime factors).

sage code - this is only for prime levels, and the focus is on ordering the values of the so you see the symmetry of the atkin-lehner operator with respect to the root number, rather than efficiency
magma code - this applies to maximal orders in definition rational quaternion algebras, and so works for levels N which are squarefree products of an odd number of primes

Acknowledgements: Much of the above code/data was produced while I was supported in part by by grants from the Simons Foundation. See my papers for more precise acknowledgements.

Kimball Martin [main] [math]
Last updated: Thu Aug 6 15:39:41 CDT 2020
kimball.martin@ou.edu