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L-Functions and Modular Forms Database
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Graded ring of classical modular forms for congruence subgroups #2627

Open jvoight opened 6 years ago

jvoight commented 6 years ago

It would be nice if on the page associated to a congruence subgroup we listed a presentation for the graded ring of modular forms for that group, with generators (preferably eigenforms, so they can be clicked on) and relations among them.

assaferan commented 2 days ago

@jvoight - I think the relevant page is now part of Modular curves, e.g. in this page the generators are written as the newforms in the Jacobian, and the relations appear as the embedded model. Does that settle this issue?

jvoight commented 15 hours ago

No, unfortunately it does not. The graded ring of modular forms is not always generated in weight 2, even when the canonical map gives a closed embedding into projective space. It is when the stack is a scheme (so no elliptic points), like for 35.48.3.a.1.

The content available in the full graded ring of modular forms is that you can get arbitrary weight k by multiplying forms. It is also a description of the stacky curve in weighted projective space, which isn't the same as the coarse space.

It's fine to leave this as v2.0.