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 modular analogue of Vinogradov’s problem on quadratic non-residue. We obtain strong explicit bounds p, depending analytic conductor for some specific choices I.