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Serre showed that for any integer Formula: see text for almost all Formula: see text where Formula: see text is the Formula: see text Fourier coefficient of any modular form with rational coefficients. In this paper, we consider a certain class of cuspforms and study Formula: see text over the set of integers with Formula: see text many prime factors. Moreover, we show that any residue class Formula: see text can be written as the sum of at most 13 Fourier coefficients, which are polynomially bounded as a function of Formula: see text
Bhakta et al. (Wed,) studied this question.