  Let $K$ be a totally real field. In this article 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, thus generalizing a theorem of Khare and Prasad. From this fact we
compute the minimal field over which a modular Jacobian becomes semi-stable.
