  We study the irreducible constituents of the reduction modulo p of
irreducible algebraic representations V of Res_{K/Q_p} GL_2 for K a finite
extension of Q_p. We show that asymptotically, the multiplicity of each
constituent depends only on the dimension of V and the central character of its
reduction modulo p. As an application, we compute the asymptotic value of
multiplicities that are the object of the Breuil-M\'ezard conjecture.
