# Classical Hecke eigenforms for $\Gamma_0(p)$.

I am in need of classical eigenforms for $\Gamma_0(p)$.

In particular I need these to be newforms for each of the even weights 8 to 26 and would settle just for cases $p=2,3$ at this moment in time. I need them in a format from which I am able to find critical L-values.

Does anyone know where to find these and/or whether MAGMA/Maple/PARI is able to compute them? (The online documentation for MAGMA doesn't seem to mention commands for finding eigen-bases)

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perhaps that Stein's tables or links at the end will help you... – Raymond Manzoni Jul 22 '12 at 11:34
William Stein's lectures Explicitly Computing Modular Forms could perhaps help you too (around page 50). William Stein is maintaining Sage (that includes Pari/Maxima and other free software...) – Raymond Manzoni Jul 22 '12 at 11:47

## 1 Answer

I think the best place to look might be the new "L-functions and modular forms database" website (still in beta at the moment). This has very detailed tables of modular forms, and, better still for your purposes, about their L-functions (critical values, first few zeros on the critical line, etc.); e.g. check out http://www.lmfdb.org/L/ModularForm/GL2/Q/holomorphic/7/4/0/a/ for lots of info about the L-function of the weight 4 level 7 eigenform.

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Ok so I understand that when the dimension is 1 we can take any such cusp form as an eigenform but what is the best way to find eigenforms when the dimension of the space of new cuspforms is not 1? – fretty Jul 23 '12 at 9:27
I don't understand your question: the website has tables of new eigenforms. – David Loeffler Jul 23 '12 at 11:10
It doesn't say that, unless I am missing something. It provides a table of new cusp forms. – fretty Jul 23 '12 at 21:16
Oh sorry I was being stupid, I realise that they are provided! – fretty Jul 23 '12 at 21:19
Do you know whether the labels given on that site can be used in MAGMA? – fretty Jul 24 '12 at 9:34