Ticket #12450 (new enhancement)

Opened 16 months ago

Last modified 16 months ago

implement the Hijikata trace formula

Reported by: was Owned by: wstein
Priority: minor Milestone: sage-5.10
Component: modular forms Keywords: trace formula, hijikata
Cc: Work issues:
Report Upstream: N/A Reviewers:
Authors: William Stein Merged in:
Dependencies: Stopgaps:

Description

This can be used for computing traces of Hecke operators acting on spaces of modular forms. In most cases, other methods are better, but this can still have value in that it can do things that are impossible with modular symbols. My pari and Magma implementations are here:  http://wstein.org/Tables/hijikata.html

Attachments

trac_12450-part1.patch Download (10.6 KB) - added by was 16 months ago.
part 1 -- this fully implements the algorithm, and includes many tests that pass (and I've tested extensively against my Magma implementation too).

Change History

Changed 16 months ago by was

part 1 -- this fully implements the algorithm, and includes many tests that pass (and I've tested extensively against my Magma implementation too).

comment:1 Changed 16 months ago by was

  • Keywords trace formula, hijikata added
  • Authors set to William Stein

Plan:

  1. Implement the algorithm and make sure it passes a wide range of tests. Done.
  1. Get coverage to 100% so it can be included in Sage.
  1. Open a new ticket to rewrite key parts using Cython and more intelligent algorithms (in some cases), which should be dramatically faster, since most of the code is simple integer manipulation.
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