  Let $\rho$ be a mod $\ell$ Galois representation attached to a newform $f$.
Explicit methods are sometimes able to determine the image of $\rho$, or even
the number field cut out by $\rho$, provided that $\ell$ and the level $N$ of
$f$ are small enough; however these methods are not amenable to the case where
$\ell$ or $N$ are large. The purpose of this short note is to establish a
sufficient condition for the image of $\rho$ to be large and which remains easy
to test for moderately large $\ell$ and $N$.
