Let f be a newform on Γ_1(N), and Vf the 2-dimensional p-adic Galois representation attached to f. Let S be a finite set of primes containing the primes divisors of Np, and denote by adV_f the adjoint of V_f. Under some mild conditions on f, we show that H_g~1(G_(Q,S),adV_f)=0. Using this result, we show that the universal deformation space of the residual representation attached to f is smooth and 3-dimensional at the point corresponding to f. When f has finite slope, one can also use this result to give a deformation theoretic description of the eigencurve of Coleman-Mazur at the point corresponding to f.
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