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 is why should this be true?

The paper can be found in following arXiv link: http://arxiv.org/pdf/math/0701478.pdf

Thanks

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

In page 2 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 is why should this be true?

The paper can be found in following arXiv link: http://arxiv.org/pdf/math/0701478.pdf

Thanks

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 is why should this be true?

The paper can be found in following arXiv link: http://arxiv.org/pdf/math/0701478.pdf

Thanks