  We prove a few results concerning the notions of finite dimensionality of
mixed Tate motives in the sense of Kimura and O'Sullivan. It is shown that
being oddly or evenly finite dimensional is equivalent to vanishing of certain
cohomology groups defined by means of Levine weight filtration. We then explain
the relation to the Grothendieck group of the triangulated category D of mixed
Tate motives. This naturally gives rise to a \lambda-ring structure on K_0(D).
