Analogue of the theta group $Γ_θ,$ II

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