Maass lifts of half-integral weight Eisenstein series and theta powers

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 $\mathrm{\infty }$ and $0$. As an application, we give explicit construction of harmonic weak Maass forms which are Hecke eigenforms and are the preimages of ${\mathrm{\Theta }}^k,k\in \{3,5,7\}$ under the shadow operator, where $\mathrm{\Theta }$ is the classical Jacobi theta function.