Fourier coefficients of forms of CM-type.

Let f be a cuspidal normalized eigenform of weight ≥ 2 for Г( N),with Fourier expansion While the Galois representations associated to f can be used effectively to study the divisibility properties of the Fourier coefficients, it is very difficult to analyze the condition a ( p) = 0 (mod p). In this paper, we show that the problem is accessible in the case that f has complex multiplication. Under some mild conditions on f, we show that for p sufficiently large, a ( p) = 0 (mod p) in fact implies that a ( p) = 0. [ABSTRACT FROM AUTHOR]