  In this paper, we explicitly construct mock modular forms whose shadows are
Eisenstein series of arbitrary integral and half-integral weight, level and
character at the cusps $\infty$ and $0$. As an application, we give explicit
construction of harmonic weak Maass forms which are Hecke eigenforms and are
the preimages of $\Theta^k, k \in \{ 3, 5, 7\}$ under the shadow operator,
where $\Theta$ is the classical Jacobi theta function.
