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Let ${\lambda }_f\left(n\right)$ be the nth normalized Fourier coefficient of a holomorphic or Maass cusp form f for SL(2,ℤ). We establish the asymptotic formula for the summatory function ${\sum }_{\begin{array}{c}n\le x\\ n\equiv l\left(modq\right)\end{array}}{\left|{\lambda }_f\left(n\right)\right|}^{2j}$ as x → ∞, where q grows with x in a definite way and j = 2,3,4.