2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62562We address the problem of the determination of the images of three-dimensional geometric and modular Galois representations. In the modular case the existence of these representations is only conjectural. We give conditions to ensure that the images are as large as possible for almost every prime. We compute some examples and stress the applications to inverse Galois theory.Number Theory11F80; 11R32; 11G35text