  Based on the values of the Weierstrass elliptic function $\wp(z|\tau)$ at
$z=\pi\tau/2$, $(\pi+\pi\tau)/{2}, (\pi+\pi\tau)/{4},(\pi+2\pi\tau)/{4}$ and
the theory of modular forms on the arithmetic group $\Gamma_0(2)$, we decompose
$\theta_2^{2n}(\tau)$ as sum of Eisenstein series and a cusp forms. Using the
recurrence relation of $\wp^{(2n)}(z|\tau)$, we provide an algorithm to
determine the exact form of these cusp forms.
