I have noticed that there are two common choices for the coefficients in defining the Chern-Simons lagrangian:

$ S(A) = \frac{k}{8\pi^2}\int_M Tr(AdA + 2/3 A^3) $ and $ S(A) = \frac{k}{4\pi}\int_M Tr(AdA + 2/3 A^3). $ What is going on here, why the two different choices? In both cases, the parameter $k$ is always integer, correct?