Let $K_f$ denote the number field generated by the Fourier coefficients $a_n$ of a normalized primitive holomorphic cusp form $f$. On page 2, line 6 of the paper mentioned in the title, Shimura writes that $K_f$ is generated by $a_p$ for almost all primes $p$. In the next sentence, he says that it follows trivially from the Multiplicity one theorem.
I don't see how it follows. I shall appreciate any comment.