Odd weight

[jvoight]

The convention for the determinant used in the current Magma code is k-1 in the exponent, not k/2. (There's only one convention that makes a graded ring under just multiplication.)

So we are for example missing the cusp form of weight 5, level 1 for QQ(sqrt(5)) described e.g. on page 124 of Bruinier's 1-2-3 of modular forms. It can be constructed as a product of theta constants, and it admits a description as a Borcherds product. It's just a square root of a cusp form in weight 10, so we could see its q-expansion easily.

At some point, we need to get our conventions right to see the forms that should be there in odd weight; this might require us to fix/add/adjust Magma code underneath.