On representations of finite groups in the space of modular forms of half-integral weight (Q1340371)

The author generalizes the work of Hecke, who investigated a representation of \(\text{SL}_ 2(\mathbb{F}_ p)\) realized in the space of modular forms of \(\Gamma_ 0(p)\) and integral weight \(k\). The author studies a representation realized in the space of modular forms of \(\Gamma_ 0(4p)\) and half-integral weight \(k + \textstyle{1\over 2}\). In particular the subrepresentation \(\rho_ f\) generated by a newform \(f\) shows a different behavior. \(\rho_ f\) is always irreducible. If \(f\) is of a Nebentype the question, whether \(\rho_ f\) is residual or non- residual, can be characterized by the eigenvalue of the Atkin-Lehner involution.