  We present a numerical algorithm for computing the spectrum of the Laplace-de
Rham operator on Calabi-Yau manifolds, extending previous work on the scalar
Laplace operator. Using an approximate Calabi-Yau metric as input, we compute
the eigenvalues and eigenforms of the Laplace operator acting on $(p,q)$-forms
for the example of the Fermat quintic threefold. We provide a check of our
algorithm by computing the spectrum of $(p,q)$-eigenforms on $\mathbb{P}^{3}$.
