In this article, we first determine a sequence $\{f_n(\tau)\}_{n\in\mathbb N}$ of modular forms with weight \[ 2^nk+4(2^{n-1}-1)\qquad(nı\mathbb N; kı\mathbb N\backslash\{1\}; \mathbb N:=\{1,2,3,\dots\}) \] We then present some applications of this sequence which are related to the Eisenstein series and the cusp forms. We also prove that higher-order derivatives of the Weierstrass type $\wp_{2n}$ functions are related to the above-mentioned sequence $\{f_n(\tau)\}_{n\in\mathbb N}$ of modular forms.