Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

HMF: simplify Hecke field polynomials #975

AurelPage opened this Issue Mar 31, 2016 · 3 comments


None yet
4 participants
Copy link

AurelPage commented Mar 31, 2016

From /roadmap: Simplify presentation of Hecke field (adjoin all elements to get an order, or mimic classical modular forms by working with the dual).


This comment has been minimized.

Copy link

edgarcosta commented May 14, 2017

An example (for future reference):

The Heck eigenvalue field of
and we should be using the integral basis computed for 6.6.50840384.1 to represent the eigenvalues.


This comment has been minimized.

Copy link

SamSchiavone commented Jul 20, 2017

I wrote a script to express the Hecke eigenvalues for Hilbert modular forms in terms of an integral basis. Given a hmfs label, the script extracts the polynomial defining the field containing the Hecke eigenvalues, runs polredabs on it, then looks up the number field in the LMFDB, extracts the integral basis stored there, and re-expresses the Hecke eigenvalues in terms of this integral basis.

  1. How would we like to display this information on the pages for the Hilbert modular forms? Maybe write alpha_1, ..., alpha_n for the elements of the integral basis and write the eigenvalues as a linear combination of them? Currently the script outputs tuples of coefficients for each eigenvalue, the number field, the field generator, and the integral basis.

  2. Should we keep track of the number fields that we find that do not have an LMFDB page? Currently the script just outputs "No number field file found in LMFDB" when this happens.


This comment has been minimized.

Copy link

edgarcosta commented Sep 15, 2017

The pr #2197 makes some progress towards this.
Perhaps we should write here, what are the next steps.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
You can’t perform that action at this time.