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

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