  Let $p$ be an odd prime and $q$ a power of $p$. We examine the deformation
theory of reducible and indecomposable Galois representations
$\bar{\rho}:G_{\mathbb{Q}}\rightarrow \text{GSp}_{2n}(\mathbb{F}_q)$ that are
unramified outside a finite set of primes $S$ and whose image lies in a Borel
subgroup. We show that under some additional hypotheses, such representations
have geometric lifts to the Witt vectors $\text{W}(\mathbb{F}_q)$. The main
theorem extends that of Hamblen and Ramakrishna in which the $n=1$ case was
treated.
