  We construct explicitly the quantization of classical linear maps of $SL(2,
R)$ on toroidal phase space, of arbitrary modulus, using the holomorphic
(chiral) version of the metaplectic representation. We show that Finite Quantum
Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent
restriction of the holomorphic quantization of $SL(2, Z)$ to the subgroup
$SL(2, Z)/\Gamma_l$, $\Gamma_l$ being the principal congruent subgroup mod l,
on a finite dimensional Hilbert space. The generators of the ``rotation group''
mod l, $O_{l}(2)\subset SL(2,l)$, for arbitrary values of l are determined as
well as their quantum mechanical eigenvalues and eigenstates.
