Let f be either a holomorphic Hecke eigenform of weight κ for SL2(ℤ) with or a Maass Hecke eigenform for SL2(ℤ) with Laplace eigenvalue ¼ + ν2. In the latter case, Here Kiν is the modified Bessel function of the third kind and e(z) = e2πiz. This paper studied the cancelation of the coefficients λ(n) or ρ(n) in nonlinear exponential sums with amplitude nθ, 0 < θ≤ ½.