I understand the association between vectors and covectors on a Riemannian manifold, but it appears that 4-momentum is given naturally as a covector, instead of vector. 4-position is clearly a vector (for that is the most natural representation of it). Similarly, 4-velocity is also vector, and given that 4-momentum is a scalar multiple of 4-velocity, one would expect 4-momentum to also be a vector. But it appears in various references as a covector by default. Is there any fundamental reason for this?