  Given a primitive, non-CM, holomorphic cusp form $f$ with normalized Fourier
coefficients $a(n)$ and given an interval $I\subset [-2, 2]$, we study the
least prime $p$ such that $a(p)\in I$ . This can be viewed as a modular form
analogue of Vinogradov's problem on the least quadratic non-residue. We obtain
strong explicit bounds on $p$, depending on the analytic conductor of $f$ for
some specific choices of $I$.

Number Theory