  We prove modularity for any irreducible crystalline $\ell$-adic odd
2-dimensional Galois representation (with finite ramification set) unramified
at 3 verifying an "ordinarity at 3" easy to check condition, with Hodge-Tate
weights $\{0, w \}$ such that $2 w < \ell$ (and $\ell > 3$) and such that the
traces $a_p$ of the images of Frobenii verify $\Q(\{a_p \}) = \Q $. This result
applies in particular to any motivic compatible family of odd two-dimensional
Galois representations of $\Gal(\bar{\Q}/\Q)$ if the motive has rational
coefficients, good reduction at 3, and the "ordinarity at 3" condition is
satisfied. As a corollary, this proves that all rigid Calabi-Yau threefolds
defined over $\Q$ having good reduction at 3 and satisfying $ 3 \nmid a_3$ are
modular.
