Analogue of the theta group $\Gamma_{\theta},$ II

TL;DR

This paper introduces the level 5 theta group, constructs associated modular forms, and computes their multiplier systems, extending the theory of theta groups and their modular properties.

Contribution

It develops the level 5 theta group and explicitly constructs modular forms with their multiplier systems, advancing the understanding of higher level theta groups.

Findings

Constructed modular forms on mma_{ heta,5}

Derived transformation formulas for theta functions with characteristics

Computed multiplier systems for the modular forms

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.