Abstract

Let K be a totally real field. We present an asymptotic formula for the number of Hilbert modular cusp forms f with given ramification at every place v of K. When v is an infinite place, this means specifying the weight of f at k, and when v is finite, this means specifying the restriction to inertia of the local Weil–Deligne representation attached to f at v. Our formula shows that with essentially finitely many exceptions, the cusp forms of K exhibit every possible sort of ramification behavior.

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