  We compute, using the method of large spin perturbation theory, the anomalous
dimensions and OPE coefficients of all leading twist operators in the critical
$ O(N) $ model, to fourth order in the $ \epsilon $-expansion. This is done
fully within a bootstrap framework, and generalizes a recent result for the
CFT-data of the Wilson-Fisher model. The anomalous dimensions we obtain for the
$ O(N) $ singlet operators agree with the literature values, obtained by
diagrammatic techniques, while the anomalous dimensions for operators in other
representations, as well as all OPE coefficients, are new. From the results for
the OPE coefficients, we derive the $ \epsilon^4 $ corrections to the central
charges $ C_T $ and $ C_J $, which are found to be compatible with the known
large $ N $ expansions. Predictions for the central charge in the strongly
coupled 3d model, including the 3d Ising model, are made for various values of
$ N $, which compare favourably with numerical results and previous
predictions.
