On the Unobstructedness of the Deformation Problems of Residual Modular Representations

Abstract

Let $f$ be a primitive form whose weight is greater than $2$. Weston [23, Theorem 1] showed that the mod $p$ representation $\bar{\rho}$ associated to $f$ is irreducible and the deformation problem for $\bar{\rho}$ is unobstructed for almost all $p$. The aim of this article is to give a simpler proof of his result in some cases.