Analogue of the theta group ${\Gamma }_{\theta },$ II

Abstract

In this series of papers, we introduce higher level versions of the theta group ${\Gamma }_{\theta }.$ In this paper, we treat the theta group of level $5$, ${\Gamma }_{\theta ,5},$ and construct modular forms on ${\Gamma }_{\theta ,5}$. Moreover we compute their multiplier systems. For this purpose, we derive transformation formula of theta function with characteristics.