Equations associated to the Principal Congruence Subgroup of Level Eight

TL;DR

This paper derives an equation related to the principal congruence subgroup of level eight without involving modular functions, aiming to deepen understanding of its algebraic structure.

Contribution

It introduces a novel equation associated with the principal congruence subgroup of level eight, avoiding the use of modular functions.

Findings

Derived a new equation for the subgroup

Provides insights into algebraic properties of the subgroup

Enhances understanding without modular functions

Abstract

The purpose of this paper is to find an equation with respect to the principal congruence subgroup of level eight without considering modular functions.