Expand BMF and ECNF/IQF data to include more fields

[JohnCremona]

Now, the data for BMF Bianchi modular forms (dimensions and rational newforms) and associated elliptic curves over imaginary quadratic fields includes 32 fields, all those of absolute discriminant up to 100 and also 163.

I have more data, for all fields of absolute discriminant up to 2000 (and going beyond that, in progress), and will upoad it. I will use this Issue to record progress.

• 1. For the 7 fields of abs disc between 100 and 120 I have data for all levels (conductors) of norm up to 1000, consisting of 5989 rational newforms and 12524 elliptic curves. These are now on beta.

• 2. For the fields of abs disc between 123 and 700 (excluding 163 for which data was there already) I have data for level norms up to 100 only. These will be next. That is about 270 fields. Now on beta.

• 3. For the fields of abs disc between 701 and 1000 I only have data for level norms up to 15, and will work on extending that to 100 if possible, though I may upload what I have already. In this smaller range there are several fields with no rational newforms (or elliptic curves), but the dimension data is still available.

• 4. For the fields of abs disc between 1000 and 2000 (about 300 more fields) I have BMF data for levels of norm up to 15, dimensions and rational newforms and elliptic curve data. This is ready for upload but is waiting until item 3 is finished and uploaded.

[JohnCremona]

As I have uploaded data, I have edited the relevant knowls. Later I'll also adjust the brows pages: on https://beta.lmfdb.org/ModularForm/GL2/ImaginaryQuadratic/ it would make sense to insert the last field for which the database has data after the three dots. Similarly on https://beta.lmfdb.org/EllipticCurve/ (and not just for imaginary quadratic fields there). This could be possibly automated, using a database query to find the largest discriminant of each base field signature.

[JohnCremona]

Update on item 3: there are still 12 fields of abs disc between 700 and 1000 where I am still working on the levels of norm up to 100 (of which 2 are still in the 70s, 2 in the 80s, 7 in the 90s and one working on levels of norm 100). That will be done by the end of 2024.

But I can add a 4th item too: for all fields of abs disc between 1000 and 2000 I have BMFs of levels of norm up to 15 (I know that 15 is a small number, but it is hard work), together with elliptic curves (for most) all ready to go into BMF and ECNF, but waiting on number 3 to finish. So that should all be done by the end of 2024 too.