Opened 11 years ago

Last modified 5 years ago

#11056 new enhancement

Wrap Cremona's code for modular forms over imaginary quadratic fields

Reported by: mraum Owned by: Martin Raum
Priority: minor Milestone: sage-wishlist
Component: modular forms Keywords:
Cc: cremona Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
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Description

Cremona has implemented some functionality for modular forms over imaginary quadratic field a long time ago. We should wrap it. Possibly we need to improve or correct some parts.

Change History (3)

comment:1 Changed 11 years ago by cremona

  • Cc cremona added; john.cremona@… removed
  • Milestone changed from sage-4.7 to sage-wishlist

Although this started a long time ago (1979) one version of my C++ code -- for the five Euclidean fields -- was the subject of my attention earlier this month, and is in quite good shape. It slots onto eclib and my intention is to add it to eclib -- which Sage already contains. Any wrapping should take place after that.

There is a second C++ version by my student Jeremy Bygott which should do everything version 1 does and more (all class number 1 fields and any class number 2 fields for which the homology information has been precomputed). This needs some attention, but has the potential to supersede version 1 for all fields of class numbers 1 and 2.

In addition, I have: two directories of Magma code, one each for the fields -23 and -31 of class number 3, written by my student Mark Lingham. I recently used these to provide Hecke eigenvalues for a paper by Pacetti at al.

Also, in Sage already my student Maite Aranes wrote completely general code for handling cusps over number fields (including Gamma_0(N)-equivalence, for example) in sage/modular/cusps_nf.py, and for M-symbols also over arbitrary fields, in sage/modular/modsym/p1list_nf.py. [Note that these two are literally for arbitrary number fields, not just imaginary quadratic fields.]

I changed the milestone to sage-wishlist!

comment:2 Changed 5 years ago by kedlaya

Status check? Is there something concrete to be done here?

comment:3 Changed 5 years ago by cremona

For the 5 Euclidean fields my C++ code is in good shape and can be found in https://github.com/JohnCremona/bianchi-progs .

For the other class number 1 fields and higher class number fields there is no change (regarding my own code) to what I wrote 5 years ago.

I have no motivation for doing this and do not know what the demand is. Even for the modular symbol code over Q, a small part of which was wrapped years ago by William and me, there has been essentially no demand for the rest to be made available through Sage.

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