On sup-norms of cusp forms of powerful level

Final version, to appear in JEMS. Please also note that the results of this paper have been significantly improved in my recent paper arXiv:1509.07489 which uses a fairly different methodologyLet f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue \lambda. It is shown that |f|_\infty 0. The exponent is further improved in the case when N is not divisible by "small squares". Our work extends and generalizes previously known results in the special case of N squarefree