Rigorous computation of Maass cusp forms of squarefree level

Abstract

We derive an algorithm to rigorously compute and verify Maass cusp forms of squarefree level and trivial character. The main tool we use is an explicit version of the Selberg trace formula with Hecke operators due to Strömbergsson. We use this algorithm to compute several thousand Maass forms for a range of levels and use this data to obtain numerical evidence towards various conjectures.

arXiv comment15 pages, 2 figures; V2: minor changes, accepted by ANTS-XV and will appear in Research in Number Theory