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
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.
This data was generated in Sage using the OU Supercomputing Center
(OSCER) for my paper:
This paper explains how this data was generated.
- text file - each line is of the form
N: d1, d2, ..., dr where N is a prime level, and the di'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
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
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:
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
- 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
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
Thu Aug 6 15:39:41 CDT 2020