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Let $f$ be a normalized Hecke eigenform with rational integer Fouriercoefficients. It is an interesting question to know how often an integer $n$has a factor common with the $n$-th Fourier coefficient of $f$. The secondauthor \cite{kumar3} showed that this happens very often. In this paper, wegive an asymptotic formula for the number of integers $n$ for which $(n,a(n))=1$, where $a(n)$ is the $n$-th Fourier coefficient of a normalized Heckeeigenform $f$ of weight $2$ with rational integer Fourier coefficients and hascomplex multiplication.

A variant of Lehmer's conjecture, II: The CM-case