Year: 2014
Type: preprint
Abstract: For prime levels $5 \le p \le 19$, sets of $Γ_{0}(p)$-permuted theta quotients are constructed that generate the graded rings of modular forms of positive integer weight for $Γ_{1}(p)$. An explicit formulation of the permutation representation and several applications are given, including a new representation for the number of $t$-core partitions. The $Γ_{0}(p)$-action induces coefficient symmetries within representations for modular forms and invariance subgroups for coupled systems of differential equations. The symmetry for levels $p = 5,7,11$ is linked to the Kleinian automorphism groups.
Source: arXiv (Cornell University)
Authors: Huber, Tim, Lara, Danny, Melendez, Esteban
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4302160701