  For every prime $p\geq 5$ for which a certain condition on the class group
$\text{Cl}(\mathbb{Q}(\mu_p))$ is satisfied, we construct a $p$-adic analytic
Galois extension of the infinite cyclotomic extension
$\mathbb{Q}(\mu_{p^{\infty}})$ with some special ramification properties. In
greater detail, this extension is unramified at primes above $p$ and tamely
ramified above finitely many rational primes and is isomorphic to a finite
index subgroup of $\text{SL}_2(\mathbb{Z}_p)$ which contains the principal
congruence subgroup. For the primes $107,139,271$ and $379$ such extensions
were first constructed by Ohtani and Blondeau. The strategy for producing these
special extensions at an abundant number of primes is through lifting
two-dimensional reducible Galois representations which are diagonal when
restricted to $p$.
