  In a previous article, we have proved a result asserting the existence of a
compatible family of Galois representations containing a given crystalline
irreducible odd two-dimensional representation. We apply this result to
establish new cases of the Fontaine-Mazur conjecture, namely, an irreducible
Barsotti-Tate $\lambda$-adic 2-dimensional Galois representation unramified at
3 and such that the traces $a_p$ of the images of Frobenii verify $\Q(\{a_p^2
\}) = \Q $ always comes from an abelian variety. We also show the non-existence
of irreducible Barsotti-Tate 2-dimensional Galois representations of conductor
1 and apply this to the irreducibility of Galois representations on level 1
genus 2 Siegel cusp forms.
