Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of n \times n matrices analogous to the classical Pick matrix. We study for which reproducing kernel Hilbert spaces it suffices to consider matrices of bounded size n . We connect this problem to the notion of subhomogeneity of non-selfadjoint operator algebras. Our main results show that multiplier algebras of many Hilbert spaces of analytic functions, such as the Dirichlet space and the Drury-Arveson space, are not subhomogeneous, and hence one has to test Pick matrices of arbitrarily large matrix size n . To treat the Drury-Arveson space, we show that multiplier algebras of certain weighted Dirichlet spaces on the disc embed completely isometrically into the multiplier algebra of the Drury-Arveson space.