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Unobstructed modular deformation problems
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 126, Number 6, December 2004
- pp. 1237-1252
- 10.1353/ajm.2004.0052
- Article
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Let f be a newform of weight k ≥ 3 with Fourier coefficients in a number field K. We show that the universal deformation ring of the mod λ Galois representation associated to f is unobstructed, and thus isomorphic to a power series ring in three variables over the Witt vectors, for all but finitely many primes λ of K. We give an explicit bound on such λ for the 6 known cusp forms of level 1, trivial character, and rational Fourier coefficients. We also prove a somewhat weaker result for weight 2.