Differential equations satisfied by modular forms of level 5

TL;DR

This paper derives the differential equations of level 5 for Eisenstein series, extending Ramanujan's classical system to a higher level, which deepens understanding of modular forms and their properties.

Contribution

It introduces the level 5 versions of Ramanujan's differential equations for Eisenstein series, expanding the theoretical framework of modular forms.

Findings

Derived differential equations for level 5 Eisenstein series

Extended Ramanujan's system to higher level forms

Provides new tools for studying modular forms of level 5

Abstract

This paper describes the derivation of the level 5 versions of Ramanujan's system of ordinary differential equations satisfied by the Eisenstein series, $E_2(q),E_4(q)$, and $E_6(q).$