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L-Functions and Modular Forms Database
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Trace forms for all newspaces of classical modular forms #2751

Open AndrewVSutherland opened 5 years ago

AndrewVSutherland commented 5 years ago

Currently we have trace forms for all newspaces of level up to 4000 and all newspaces where we have computed newforms for the space. But there are newspaces in our Nk^2 <= 40000 box that do not meet either of these criteria but do have home pages, for example:

http://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/9887/2/c/

It would be nice to have trace forms for these, but given the dimension (over 4 million in this case) this will require a new computational approach (writing down the matrix of even a single Hecke operator may be infeasible).

JohnCremona commented 5 years ago

Why is that specific space there? Some special interest? I would really like us to have N=1225, k=2 and (at least) the character of order 8 and conductor 35. If we allow some spaces of special interest, can we add it? (I would also like the newform orbit of dimension 8, not just the space).

AndrewVSutherland commented 5 years ago

@JohnCremona The feature request is that all newspaces with a home page should have a trace form (including all newspaces of level 1225 and weight 2, although I'm slightly confused by what you wrote because there are no Dirichlet characters of conductor 35 and order 8: http://www.lmfdb.org/Character/Dirichlet/?modulus=1225&conductor=35).

I listed the particular example I did just to give an indication that simply asking Sage/Magma/Pari to compute the trace form may not be feasible, a new algorithm may be required.

JohnCremona commented 5 years ago

@JohnCremona The feature request is that all newspaces with a home page should have a trace form (including all newspaces of level 1225 and weight 2, although I'm slightly confused by what you wrote because there are no Dirichlet characters of conductor 35 and order 8: http://www.lmfdb.org/Character/Dirichlet/?modulus=1225&conductor=35).

Sorry, I meant order 4. It's the product of the mod 5 cyclotomic and mod 7 quadratic characters: http://www.lmfdb.org/Character/Dirichlet/1225/293 or its conjugate.