We investigate the automorphic spectra of the natural weighted adjacency operator on the complex
arising as a
quotient of an
-type
building. We prove that the set of nontrivial approximate eigenvalues
of the weighted
adjacency operators
on the quotient induced from the colored adjacency operators
on the building
for
contains the
simultaneous spectrum of
and another hypocycloid with three cusps. As a byproduct, we reestablish a proof of the
fact that
is not a Ramanujan complex, from a combinatorial aspect.