Conjecture on density of non-degenerate Picard-group eigenvalues

Let the Picard group be the arithmetic group underlying the spectrum of the Laplacian, and consider the sequence of its non-degenerate eigenvalues. Conjecture on density of non-degenerate Picard-group eigenvalues. The sequence of non-degenerate eigenvalues in the spectrum of the Laplacian for the Picard group has density zero. The paper motivates this claim using Weyl's law and Steil's theorem: the symmetry classes occur with equal leading-order density, while the theorem forces degeneracies among the relevant classes.