On the image of the residual representation attached to a CM form - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T22:47:22Z http://mathoverflow.net/feeds/question/88623 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88623/on-the-image-of-the-residual-representation-attached-to-a-cm-form On the image of the residual representation attached to a CM form unramified 2012-02-16T12:04:19Z 2012-02-16T14:07:09Z <p>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.</p> http://mathoverflow.net/questions/88623/on-the-image-of-the-residual-representation-attached-to-a-cm-form/88629#88629 Answer by David Loeffler for On the image of the residual representation attached to a CM form David Loeffler 2012-02-16T14:07:09Z 2012-02-16T14:07:09Z <p>No. For instance there are plenty of modular forms that are not CM, but are congruent mod p to CM forms or to Eisenstein series, and thus whose residual Galois representations have small image.</p>