On the number of dominating Fourier coefficients of two newforms

Let f = ∑ n≥1 λf (n)n (k1−1)/2qn and g = ∑ n≥1 λg(n)n (k2−1)/2qn be two newforms with real Fourier coeffcients. If f and g do not have complex multiplication and are not related by a character twist, we prove that #{n ≤ x | λf (n) > λg(n)} x.