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Wrap Cremona's code for modular forms over imaginary quadratic fields #11056

Closed 18d65770-dc1e-4813-89a9-4828e4aae4a9 closed 3 days ago

18d65770-dc1e-4813-89a9-4828e4aae4a9 commented 13 years ago

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.

CC: @JohnCremona

Component: modular forms

Issue created by migration from https://trac.sagemath.org/ticket/11056

JohnCremona commented 13 years ago
comment:1

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!

kedlaya commented 8 years ago
comment:2

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

JohnCremona commented 8 years ago
comment:3

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.

JohnCremona commented 3 days ago

Update: the repository cited above now contains code to handle all imaginary quadratic fields of absolute discriminant up to 2100 (for which the necessary precomputation has been done and is stored in data files in that repository), and all others (in principle, though the precomputation which then needs to be done, once, takes between 30 minutes and a few days). But I am still not convinced that having this large amount of C++ code available from Sage is in demand, so I still do not plan to do this. Given that no-one has commented on this ticket in over 8 years, I think I will close it.