  The main goal of this paper is to prove existence of $p$-adic lifts of even
Galois representations in balanced global settings with dual Selmer groups of
rank one, and to construct examples of even residual representations in
characteristic $p=3$ for which the theorem yields existence of $3$-adic lifts.
In the proof of the main theorem, we show that if the global deformation rings
are not flat over $\mathbb{Z}_p$ at the minimal level, then after allowing
ramification at one auxiliary prime, the new parts of the global rings enjoy
the flatness property. The proof is independent of the parity of the
representations. Previously, flatness was only known in established cases of
Langlands reciprocity in the odd parity, while it is new for even deformation
rings in balanced global settings of rank one. As a corollary, we show that by
choosing the auxiliary prime appropriately, we can control the rank mod $p$ of
the new part of the flat ring. The examples of $3$-adic representations and
flat, even deformation rings are built by applying techniques from global class
field theory to a family of totally real fields studied by D. Shanks. In the
process of constructing the even residual representations, we show that there
exist cuspidal automorphic representations $\pi$ and $\pi'$ of
$\operatorname{GL}(2,\mathbb{A}_{\mathbb{Q}})$ attached to classical Maass wave
forms of level $\ell=20887$ whose mod 3 reductions are distinct. The proof
applies a theorem of R. P. Langlands from his theory of base change.
