On spaces of modular forms spanned by eta-quotients

By Jeremy A. Rouse, J. J. Webb. 2013

61 citations recorded by the source corpus.

Abstract An eta-quotient of level N is a modular form of the shape f ( z ) = ∏ δ | N η ( δ z ) r δ . We study the problem of determining levels N for which the graded ring of holomorphic modular forms for Γ 0 ( N ) is generated by (holomorphic, respectively weakly holomorphic) eta-quotients of level N. In addition, we prove that if f ( z ) is a holomorphic modular form that is non-vanishing on the upper half plane and has integer Fourier coefficients at infinity, then f ( z ) is an integer multiple of an eta-quotient. Finally, we use our results to determine the structure of the cuspidal subgroup of J 0 ( 2 k ) ( Q ) .

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8d7a8a25693bd3921a2a0d298e18d08e56f323e8