Dear Professor,
Thank you for the reply. Actually, I meant mfeigenbasis gives eigenforms for the newspace. Say, I consider the space mf = mfinit([7, 3, -7]) and use mf1 = mfeigenbasis(mf). Then, the dimension of mf1 is 1 and it correspond to the newform
eta(z)^3 * eta(7z)^3, whereas the space mf has a basis comprising of three normalized Hecke eigenforms. So, that is what I was trying to figure out if there is a way to find all of them explicitly, given any k, N and character.
I am sorry if I misunderstood what you were trying to say.
Thanks,
Swati
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Dear Swati,
You can recursively obtain all the eigenforms by using the newforms of lower level and the mfbd operator.
However, you are pointing at a problem: the documentation of mfeigenbasis does not say that it only computes the newforms, it says "eigenforms". We should probably either fix the doc or implement eigenforms for other spaces than the newspace.
Cheers,
Aurel
On 13/11/2024 23:03, LNU, Swati wrote:
Hello,
Given any space M_{k}(N, \chi) for large k and N, is there a way to determine using PARI/GP the basis of normalized Hecke eigenforms (explicitly) for the entire space? I know mfeigenbasis() just determines the basis for the newspace.
Thanks,
Swati
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