Let f be a primitive Hilbert modular form over F of weight k with coefficient field Ef, generated by the Fourier coefficients C(p, f) for p ∈ Spec(OF). Under certain assumptions on the image of the residual Galois representations attached to f, we calculate the Dirichlet density of {p ∈ Spec(OF)|Ef = Q(C(p, f))}. For k = 2, we show those assumptions are satisfied when [Ef : Q] = [F : Q] is an odd prime. We also study analogous results for Ff, the fixed field of Ef by the set of all inner twists of f. Then, we provide some examples of f to support our results. Finally, we compute the density of {p ∈ Spec(OF)|C(p, f) ∈ K} for fields K with Ff ⊆ K ⊆ Ef © 2022 Cambridge University Press. All rights reserved.