Modular forms, particularly cusp forms, are ubiquitous objects in mathematics. A natural way to understand a cusp form is to study its L-p norms, for in principle the distribution of a function can be recovered from the knowledge of its moments. In this talk I will describe a new bound for the L-4 norm of a cusp form of prime level q, as q tends to infinity. This work is joint with Jack Buttcane.

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