downloading q-expansion coefficients

[Axel Ciceri]

Hi,

 

I was wondering if you could help me with something. I am trying to download a dataset of q-expansion coefficients up to some order for a large number of modular forms. Can this be done directly from the LMFDB website?

 

Thanks,

Axel

 

[Andrew Sutherland]

It depends on what you mean by a large number.  There are two API interfaces available at https://www.lmfdb.org/api/ and https://www.lmfdb.org/api2/ that can be used to download data for up to 100 forms per call from any table (the first API is simpler to use but does not support as rich a set of options as the second).

But the there are more than 14 million embedded modular forms in the database, so these won't be useful ways to download a substantial proportion of them.

Also, note that we provide q-expansions in two formats: for modular forms whose coefficient fields have degree at most 20 you can download the coefficients as algebraic integers.  These are stored in the table mf_hecke_nf, see https://www.lmfdb.org/api/mf_hecke_nf/, with a single entry for each Galois orbit.  Complex coefficients are available for every modular form in the table mf_hecke_cc, see https://www.lmfdb.org/api/mf_hecke_cc/.

Andrew Sutherland