  We calculate CFT data for the Gross-Neveu model in $2<d<4$ dimensions at the
next-to-leading order in the $1/N$ expansion. In particular, we make use of the
background field method to derive various conformal triangles involving the
composite operator $s^2$, for the Hubbard-Stratonovich field $s$. We then apply
these conformal triangles to obtain the corresponding OPE coefficients.
