  We present explicit formulas for the spectra of higher spin operators on the
subbundle of the bundle of spinor-valued trace free symmetric tensors that are
annihilated by the Clifford multiplication over the standard sphere in odd
dimension. In even dimensional case, we give the spectra of the square of such
operators. The Dirac and Rarita-Schwinger operators are zero-form and one-form
cases, respectively. We also give eigenvalue formulas for the conformally
invariant differential operators of all odd orders on the subbundle of the
bundle of spinor-valued forms that are annihilated by the Clifford
multiplication in both even and odd dimensions on the sphere.
