  The modular properties of some higher dimensional varieties of special Fano
type are analyzed by computing the L-function of their $\Omega-$motives. It is
shown that the emerging modular forms are string theoretic in origin, derived
from the characters of the underlying rational conformal field theory. The
definition of the class of Fano varieties of special type is motivated by the
goal to find candidates for a geometric realization of the mirrors of rigid
Calabi-Yau varieties. We consider explicitly the cubic sevenfold and the
quartic fivefold, and show that their motivic L-functions agree with the
L-functions of their rigid mirror Calabi-Yau varieties. We also show that the
cubic fourfold is string theoretic, with a modular form that is determined by
that of an exactly solvable K3 surface.
