A Maass Lifting of $Theta^3$ and Class Numbers of Real and imaginary Quadratic Fields

We give an explicit construct of a harmonic weak Maass form $F_{Theta}$ that is a lift of $Theta^3$, where $Theta$ is the classical Jacobi theta function. Just as the Fourier coefficients of $Theta^3$ are related to class numbers of imaginary quadratic fields, the Fourier coefficients of the holomorphic part of $F_{Theta}$ are associated to class numbers of real quadratic fields.