Classification of half-integral weight hecke eigenforms which are dedekind-eta quotients

Modular forms and, in particular, Hecke eigenforms come to the fore with their interesting properties in number theory. For example, the Sato-Tate Theorem, which is the most important result of recent years in mathematics, is valid only for Hecke eigenforms. The problem of systematic selection of Hecke eigenforms is a critical step in obtaining statistical results, especially on half-integral weight Hecke eigenforms. There are studies in the literature on the subject. Another solution to the problem can be Dedekind-eta products. In this study, which consists of three parts, the problem of classification of Hecke eigenforms consisting of Dedekind-eta products is discussed. In the first chapter, modular forms, which are the basis of the subject, are introduced and their basic features are examined. The second section is devoted to Dedekind-eta products, and in the third section, which constitutes the original part of the study, a special classification of Hecke eigenforms consisting of Dedekind-eta products is obtained.