Let f be a newform for Γ₁(N). There is attached to f a family of Galois representations with ℓ-adic coefficients. Calculating these Galois representations seems intractable, but if we only ask for the local Galois representations at a particular prime p ≠ ℓ, then we are led into some rather interesting territory, especially if p² divides N. These local representations are parametrized by certain infinite-dimensional representations of GL₂(Q_p), according to the Local Langlands Correspondence. We show how to use Magma to determine these "local components". The computation involves working with modular symbols as well as with representations of finite matrix groups.