  Let $ F$ be an imaginary quadratic field and $\mathcal{O}$ its ring of
integers. Let $ \mathfrak{n} \subset \mathcal{O} $ be a non-zero ideal and let
$ p> 5$ be a rational inert prime in $F$ and coprime with $\mathfrak{n}$. Let $
V$ be an irreducible finite dimensional representation of $
\bar{\mathbb{F}}_{p}[{\rm GL}_2(\mathbb{F}_{p^2})].$ We establish that a system
of Hecke eigenvalues appearing in the cohomology with coefficients in $ V$
already lives in the cohomology with coefficients in $
\bar{\mathbb{F}}_{p}\otimes det^e$ for some $ e \geq 0$; except possibly in
some few cases.
