m ashrafi - Department of Physics, Isfahan University of Technology, Isfahan, Iran

Modular invarinat, constraints the spectrum of the theory. Using the medum temprature expansion, for first and third order of derivative, a universal upper bound on the lowest primary field has been obtained in recent researches. In this paper, we will improve the upper bound, on the scaling dimension of the lowest primary field. We use by the medium temprature expansion for an arbitrary order of derivatives. We show that the upper bound depends on the order of derivative. In this research, we obtain the optimal values of the order of derivatives which leads to the best upper bound

Conformal Field Theory (CFT), modular invariant, medium temprature expansion