A classification of even representations onto 3-adic SL(2)

TL;DR

This paper classifies even representations onto SL(2, Z_3) with prime conductor and provides an explicit algorithm based on global class field theory to compute all such representations.

Contribution

It introduces a classification of even representations onto SL(2, Z_3) and presents an explicit algorithm for their computation.

Findings

Complete classification of even representations for prime conductor

Development of an explicit algorithm based on class field theory

Comprehensive enumeration of such representations

Abstract

This paper gives a classification of even representations onto $\operatorname{SL}(2,\mathbb{Z}_3)$ of prime conductor. In addition, an explicit algorithm based on global class field theory is exhibited, computing an exhaustive series of such even representations.