Abstract. In this paper, by using the modular forms of weight nk (2 ≤ n ∈ N and k ∈ Z), we construct a formula which generates modular forms of weight 2nk + 4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function j 4 , we obtain the Fourier coefficients of modular forms with weight 4.