A Dimension Formula for Modular Forms
The goal of this paper is to establish a dimesion formula for two classes of modular forms on the full modular group. Modular Forms are a class of analytic functions on the upper half of the complex plane. These functions are of great interest in number theory research due to their symmetry properties. We will first discuss the definition of a modular form and the terminology necessary to understand the definition. We will then define two specific types of modular forms, entire forms and cusp forms before discussing a set of entire forms, the Eisenstein Series and a cusp form, the Discriminant function. Finally we will use these two types of functions to establish a dimension formula for the vector spaces of entire and cusp modular forms on the full modular group.
Franklin and Marshall College Archives, Undergraduate Honors Thesis 2018
- F&M Theses Collection