  We consider certain modules of the symmetric groups whose basis elements are
called tabloids. Some of these modules are isomorphic to subspaces of the
cohomology rings of subvarieties of flag varieties as modules of the symmetric
groups. We give a combinatorial description for some weighted sums of their
characters, i.e., we introduce combinatorial objects called
$(\rho,\Ll)$-tabloids and rewrite weighted sums of characters as the numbers of
these combinatorial objects. We also consider the meaning of these
combinatorial objects, i.e., we construct a correspondence between
$(\rho,\Ll)$-tabloids and tabloids whose images are eigenvectors of the action
of an element of cycle type $\rho$ in quotient modules.
