We consider automorphy of many representations of the form

\rhoba:G_K ---> PGL_2(k) with K a CM field and k=F_3,F_5.

In particular we prove (under some mild conditions) that for F totally real, a surjective representation

\rho:G_F ---> PGL_2(F_5)

with totally odd sign character arises from a Hilbert modular form of weight (2,\ldots, 2).

This is an apparently new case of the Buzzard-Diamond-Jarvis conjectures which extend Serre's modularity conjecture to totally real fields.

This is based on joint work with Patrick Allen (UIUC) and Jack Thorne (Cambridge).