Congruence covers of triangular modular curves and their Galois groups

TL;DR

This paper computes the Galois groups of congruence covers related to hyperbolic triangle groups and determines the genera of the resulting modular curves, advancing understanding of their algebraic and geometric properties.

Contribution

It provides explicit calculations of Galois groups for congruence covers of triangular modular curves, a novel contribution in this area.

Findings

Galois groups of specific congruence covers are explicitly determined.

Genus values of the associated modular curves are deduced.

Results enhance understanding of the algebraic structure of these curves.

Abstract

This article computes the Galois groups of congruence covers arising in the context of certain hyperbolic triangle groups. As a consequence of this computation, the genera of the respective curves are deduced.