  We prove automorphy lifting results for geometric representations $\rho:G_F
\rightarrow GL_2(\mathcal{O})$, with $F$ a totally real field, and
$\mathcal{O}$ the ring of integers of a finite extension of $\mathbb{Q}_p$ with
$p$ an odd prime, such that the residual representation $\bar{\rho}$ is totally
odd and induced from a character of the absolute Galois group of the quadratic
subfield $K$ of $F(\zeta_p)/F$. Such representations fail the Taylor-Wiles
hypothesis and the patching techniques to prove automorphy do not work. We
apply this to automorphy of elliptic curves $E$ over $F$, when $E$ has no $F$
rational 7-isogeny and such that the image of $G_F$ acting on $E[7]$ normalizes
a split Cartan subgroup of $GL_2(\mathbb{F}_7)$.
