Appears in collection : Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

A major achievement of modern number theory is the proof of a bijection between odd, irreducible, 2-dimensional Artin representations and holomorphic weight 1 Hecke eigenforms. Despite this result, concrete examples have proven difficult to produce owing to weight 1 being non-cohomological, and the contribution to the discrete spectrum from modular forms being inseparable from the contribution from Maass forms. In this talk, I will cover recent work towards an improved method for computing weight 1 forms, and report on the implementation of this method by which we computed all such forms up to level 10,000.