Let

\begin{align*} \rho: G_{\mathbb Q} \to GL_n(\overline{\mathbb Q}_\ell) \end{align*}

be continuous, irreducible, geometric, and unramified outside finitely many primes. The Fontaine-Mazur Conjecture predicts that $\rho$ occurs as a subquotient of the $\ell$-adic cohomology of an algebraic variety over $\mathbb Q$, after allowing the standard Tate twists. In the two-dimensional odd case over $\mathbb Q$, this geometric origin is expected to force an association with a cuspidal modular eigenform, up to finite-order twists and Tate twists.