Erraneous decomposition of oldform spaces

[Jakob Burgi]

Dear support team,

all webpages of the form "Space of modular forms of level ? and weight ?" that discuss a non-trivial space of oldforms, such as https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/4/8/, seem to contain an error in the section "Decomposition of S_k^old(Gamma) into lower level spaces": in fact, the newspace S_k^old(Gamma) is contained in the decomposition of the oldspace S_k^old(Gamma) of the same level. This is wrong, as S_k^old(Gamma) and S_k^new(Gamma) are orthogonal to each other w.r.t the Peterson inner product. The solution to this, in my opinion, is to not include S_k^new(Gamma) in the decomposition of S_k^old(Gamma).

Best,

Jakob Burgi

[Edgar Costa]

Thanks, Jakob.

I have created the issue: https://github.com/LMFDB/lmfdb/issues/6319 where we will track the progress of fixing this.

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