  We show that a sufficient condition for an irreducible automorphic Galois
representation $\rho: G_F\to\mathrm{GL}_2({\overline{{\bf F}}_p})$ of a totally
real field $F$ to have an automorphic crystalline lift is that for each place
$v$ of $F$ above $p$ the restriction $\mathrm{det}\rho|_{I_v}$ is a fixed power
of the mod $p$ cyclotomic character. Moreover, we show that the only
obstruction to controlling the level and character of such automorphic lifts
arises for badly dihedral representations.
