|
6
|
In page 3 of Kilford's paper generating spaces of modular forms with $\eta$-products, he mentions that there are only finitely many spaces of modular forms that can be completely generated by $\eta$-products. My question why is this true? The paper can be found in following arXiv link: http://arxiv.org/pdf/math/0701478.pdf Thanks |
|||
|
|
|
6
|
There's a brief answer to this on page 3 of the paper; there are only finitely many eta-products with q-valuation 1 (one can write them all down), these all have a given level, so other levels will have a form with q-valuation 1 which can't be written as an eta-product. Note that I defined eta-products to be products of eta-functions with non-negative exponents. |
|||
|
