The spectrum of the Laplace operator on connected compact simple Lie groups of rank four

In the present article, we explicitly compute the spectrum of the Laplace operator on smooth real-valued and complex-valued functions on connected compact simple Lie groups of rank four with a bi-invariant Riemannian metrics that correspond to the root systems $B_4$, $C_4$, and $D_4$. We also find a connection between the obtained formulas, number theory, and integral quadratic forms in two, three, and four variables.