  Let $U/K$ be a smooth affine curve over a number field and let $L$ be an
irreducible rank 3 $\overline{\mathbb Q}_{\ell}$-local system on $U$ with
trivial determinant and infinite geometric monodromy around a cusp. Suppose
further that $L$ extends to an integral model such that the Frobenius traces
are contained in a fixed totally real number field. Then, after potentially
shrinking $U$, there exists an abelian scheme $f\colon B_U\rightarrow U$ such
that $L$ is a summand of $R^2f_*\overline{\mathbb Q}_{\ell}(1)$.
  The key ingredients are: (1) the totally real assumption implies $L$ admits a
square root $M$; (2) the trace field of $M$ is sufficiently bounded, allowing
us to use recent work of Krishnamoorthy-Yang-Zuo to construct an abelian scheme
over $U_{\bar K}$ geometrically realizing $L$; and (3) Deligne's
weight-monodromy theorem and the Rapoport-Zink spectral sequence, which allow
us to pin down the arithmetizations using the total degeneration.
