Error in definition of newform subspace

[Judith Ludwig]

Dear LMFDB team,

I think the definition of the newform subspace, as it currently appears on the LMFDB is wrong. When clicking on Classical MFs, then on Galois orbits, and then on newform subspace, the following definition appears:

"The newform subspace of newform … is the subspace generated by T_p(f) for all Hecke operators T_p for p caprice to the level, equivalently, the subspace generated by the Galois conjugates of f.“

While I agree with „the Galois conjugates of f“, the first part is off. The modular form f is a newform, hence f is an eigenform for all the T_p, hence T_p(f) is just a_p(f) f.

I just finished teaching a course on modular forms at Heidelberg University and one of my goals was to teach them the concepts that appear in the classical modular forms section of the LMFDB, so that my students can make sense of the data. This is why I looked at the definitions.

Best wishes,

Judith Ludwig

[Andrew Sutherland]

Thank you for letting us know!  I'm not sure what happened here, but this has been fixed on beta (see https://beta.lmfdb.org/knowledge/show/cmf.newform_subspace) and should automatically propogate to www.lmfdb.org.