On the computation of coefficients of modular forms: the reduction modulo p approach

Jinxiang Zeng, Linsheng Yin

Published 2012-11-06, updated 2013-05-17Version 4

In this paper we present a probabilistic algorithm to compute the coefficients of modular forms of level one. Focus on the Ramanujan's tau function, we give out the explicit complexity of the algorithm. From a practical viewpoint, the algorithm is particularly well suited for implementations.