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For classical modular forms, the correspondence between the form having CM by an imaginary quadratic field $K$ and it being induced from a Hecke character on $K$ is well-known. (Ribet's paper is a standard reference.)
I am looking for a reference for the analogous result for Hilbert modular forms over a totally real field F. In particular, if the form has CM then it arises from a Hecke character on a quadratic imaginary extension $K$ (over $F$.) I believe, for the converse, Yoshida/Hida is the reference. Thanks