On The Hecke Eigenforms of Half-Integral Weight and Dedekind-Eta Products

TL;DR

This paper classifies Dedekind-eta products of half-integral weight that are Hecke eigenforms up to weight 15/2, using the Shimura lift, contributing to the understanding of modular forms.

Contribution

It provides a complete classification of Dedekind-eta products as Hecke eigenforms in a specific weight range, a novel systematic approach.

Findings

Identified all Dedekind-eta products of half-integral weight up to weight 15/2 that are Hecke eigenforms.

Used Shimura lift to establish the classification.

Enhanced understanding of the structure of modular forms of half-integral weight.

Abstract

Systematic choice of the Hecke eigenforms of half-integral weight is an interesting problem in the theory of modular forms. In this paper, we find all Dedekind-eta products of half-integral weight which are Hecke eigenforms up to weight 15/2 with varying levels. Proof is based on the Shimura lift.