Computing Euler products and coefficients of classical modular forms for twisted L-functions

TL;DR

This paper presents an efficient algorithm for rapidly computing extensive coefficients of classical modular forms and demonstrates its application to Euler products and triple product L-functions of large conductor.

Contribution

The paper introduces a complete, fast algorithm for computing modular form coefficients and applies it to complex L-function calculations, advancing computational number theory methods.

Findings

Efficient computation of millions of modular form coefficients in seconds.

Successful calculation of triple product L-functions with large conductors.

Enhanced understanding of Euler product operations through practical algorithms.

Abstract

We describe a complete algorithm to compute millions of coefficients of classical modular forms in a few seconds. We also review operations on Euler products and illustrate our methods with a computation of triple product L-function of large conductor.