Computing characteristic polynomials of Hecke operators when the weight is large

William A. Stein

Abstract

We describe an algorithm that computes the Hecke operator T_p,k on weight-k modular forms on SL₂(Z). This algorithm is targeted at the case when both p and k are large. The algorithm generalizes to higher level.

This paper isn't quite done, because I still want to add some numerical examples.

highweight.dvi
highweight.tex macros.tex biblio.bib
implement.m (The implementation in the above dvi file.)
genspace.m (I mess of code that I used when developing the algorithm.)

Last modified: 9 February 2001