Conformal symmetry of the critical point is usually left unused in the perturbative computations of the epsilon expansion series for the Wilson-Fisher fixed point. Conformal bootstrappers would love to do the exact opposite -- to reproduce the epsilon expansion from conformal field theory only, without any input from perturbation theory. Here we will present a modest initial result in this direction -- use conformal symmetry to derive the anomalous dimensions of $\varphi^n$ at the lowest nontrivial order. The recombination of the conformal multiplets of $\varphi$ and $\varphi^3$ will play a key role.