  Consider the semisimple mod p reduction of the Galois representation
associated to a Hilbert newform f by Carayol and Taylor. This paper discusses
how, under certain conditions on f, the universal ring for deformations of this
residual representation with fixed determinant is unobstructed for almost all
primes. We follow the approach of Weston, who carried out a similar program for
classical modular forms in 2004. As such, the problem essentially comes down to
verifying that various local invariants vanish at all places dividing p or the
level of the newform. We conclude with an explicit example illustrating how one
can in principle find a lower bound on p such that the universal ring for
deformations of the residual representation attached to f with fixed
determinant is unobstructed for all primes over p.
