Solution
= Solution
Applying <Wick theorem> to the stated <holomorphic stress-energy tensor> gives
$$
T(z)\gamma(w)\sim
\frac{h\gamma(w)}{(z-w)^2}+\frac{\partial\gamma(w)}{z-w},
$$
and
$$
T(z)\beta(w)\sim
\frac{(1-h)\beta(w)}{(z-w)^2}+\frac{\partial\beta(w)}{z-w}.
$$
These are exactly the stress-tensor OPEs of <primary operators>. Hence $\gamma$ has holomorphic <conformal weight> $h$ and $\beta$ has weight $1-h$.