  This paper studies crystalline representations of G_K with coefficients of
any dimension, where K is the unramified extension of Q_p of degree a. We prove
a theorem of Fontaine-Laffaille type when \sigma-invariant Hodge-Tate weight
less than p-1, which establishes the bijection between Galois stable lattices
in crystalline representations and strongly divisible \phi-lattice. In
generalizing Breuil's work, we classify all reducible and irreducible
crystalline representations of G_K of dimensional 2, then describe their mod p
reductions. We generalize some results (of Deligne, Fontaine-Serre, and
Edixhoven) to representations arising from Hilbert modular forms when
\sigma-invariant Hodge-Tate weight less than p-1.
