Ramification of the eigencurve at classical RM points

J.Bellaïche and M.Dimitrov have shown that the -adic eigencurve is smooth but not étale over the weight space at -regular theta series attached to a character of a real quadratic field in which splits. In this paper we prove the existence of an isomorphism between the subring fixed by the Atkin-Lehner involution of the completed local ring of the eigencurve at these points and an universal ring representing a pseudo-deformation problem. Additionally, we give a precise criterion for which the ramification index is exactly . We finish this paper by proving the smoothness of the nearly ordinary and ordinary Hecke algebras for Hilbert modular forms over at the overconvergent cuspidal Eisenstein points, being the base change lift for of these theta series. Our approach uses deformations and pseudo-deformations of reducible Galois representations.