On sup-norms of cusp forms of powerful level

Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue λ. It is shown that |f|_\infty <<_{λ, ε} N^{-1/12 + ε} for any ε>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.

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