  This paper aims to provide an explicit computation of the equivariant
noncommutative residue density of which yield the metric and Einstein tensors
on even-dimensional Riemannian manifolds. A considerable contribution of this
paper is the development of the spectral Einstein functionals by two vector
fields and the equivariant Bismut Laplacian over spinor bundles. We prove the
equivariant Dabrowski-Sitarz-Zalecki type theorems for lower dimensional spin
manifolds with (or without) boundary.
