  Using Operator Product Expansions and a graphical ansatz for the four-point
function of the fundamental field \phi^{\alpha}(x) in the conformally invariant
O(N) vector model, we calculate the next-to-leading order in 1/N values of the
quantities C_{T} and C_{J}. We check the results against what is expected from
possible generalisations of the C- and k-theorems in higher dimensions and also
against known three-loop calculations in a O(N) invariant \phi^{4} theory for
d=4-\epsilon.
