[@Sengun] and the work of the first author ([@CremonaTessellations], [@CremonaTwist], [@Cremona-Whitley]). For our purposes we may restrict our attention to the space $S_2(\id{n})$ of Bianchi modular forms which are cuspidal and of weight $2$ for the congruence subgroup $\Gamma_0(\id{n})\leq\operatorname{GL}_2({{\mathcal{O}}}_K)$, where the level $\id{n}\subseteq{{\mathcal{O}}}_K$ is an integral ideal of $K$. This space is a finite-dimensional vector space equipped with a Hecke action. Its newforms subspace is spanned by eigenforms which are simultaneous eigenvectors for the algebra of Hecke operators. Bianchi modular forms can also be seen within the context of cohomological automorphic forms, since we have the isomorphism $S_2(\id{n})\cong H^1(Y_0(\id{n}),\C)$, where $Y_0(\id{n})$ is the quotient of hyperbolic $3$-space $\mathcal{H}_3$ by $\Gamma_0(\id{n})$. A more concrete description of these Bianchi modular forms is as real analytic functions $\mathcal{H}_3\to\C^3$ satisfying certain conditions. In the work of the second author and his students ([@CremonaTessellations], [@Cremona-Whitley]) explicit methods were developed to compute the spaces $S_2(\id{n})$ over $K$ for each of the nine imaginary quadratic fields $K$ of class number $1$. Recall that the orders of the isotropy groups of points of $Y_0(1)$ are only divisible by the primes $2$ and $3$, hence for $\ell \ge 5$ the cohomology $H^1(Y_0(1),\F_\ell)$ matches the group cohomology $H^1(\operatorname{PGL}_2({{\mathcal{O}}}_K),\F_\ell) = H^1(\operatorname{PGL}_2({{\mathcal{O}}}_K),\Z)\otimes 