  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
Str\"{o}mbergsson. 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.
