# On the image of the residual representation attached to a CM form

It is a classical result of Ribet that if an eigenform has CM the its residual projective image is "small" (cyclic or dihedral.) Is the converse true, i.e, if f is a form whose associated residual Gal representation has "small" projective image then f has CM? Thanks.

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I learned this from pages 4-5 of an article of Ribet: math.berkeley.edu/~ribet/Articles/rankin.pdf. His method seems somewhat qualitative, but the remark at the top of page 6 suggests that one might be able to get more precise control on these primes, at least when $p>k+1$ and does not divide the level. –  Kevin Ventullo Feb 17 '12 at 23:51