Kieran Child

University of Bristol

Computation of weight 1 modular forms

Linfoot Number Theory Seminar

4th May 2022, 11:00 am – 12:00 pm
Fry Building, Room 2.04

A major achievement of modern number theory is the proof of Artin's conjecture in the odd, 2-dimensional case. This establishes a bijection between "weight 1 newforms of level N and character χ" and "odd, 2-dimensional, irreducible Artin representations with conductor N and determinant character χ." Despite this incredible result, concrete examples have been difficult to construct, with the computation of weight 1 modular forms lagging behind computation of all other weights. In this talk, I will present several optimisations to the computation of weight 1 newforms, which enabled us to produce for the first time Fourier expansions of all such forms up to level 10,000.

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