Kieran Child

Twist-minimal trace formula for holomorphic cusp forms

The coefficients of holomorphic modular forms constitute arithmetic data for many different problems, including counting points on elliptic curves, representing integers by quadratic forms, and classifying Galois representations. The Eichler-Selberg trace formula provides an explicit formula for computing this data, but the terms involved are computationally expensive and this problem compounds when computing weight-1 forms. In this talk, I will explain how we use a twist-minimal decomposition to derive and implement a more efficient computation of arbitrary cuspform spaces, including weight-1 spaces.