  In this paper, we use the theory of deformation quantization to understand
Connes' and Moscovici's results \cite{cm:deformation}. We use Fedosov's method
of deformation quantization of symplectic manifolds to reconstruct Zagier's
deformation \cite{z:deformation} of modular forms, and relate this deformation
to the Weyl-Moyal product. We also show that the projective structure
introduced by Connes and Moscovici is equivalent to the existence of certain
geometric data in the case of foliation groupoids. Using the methods developed
by the second author \cite{t1:def-gpd}, we reconstruct a universal deformation
formula of the Hopf algebra $\calh_1$ associated to codimension one foliations.
In the end, we prove that the first Rankin-Cohen bracket $RC_1$ defines a
noncommutative Poisson structure for an arbitrary $\calh_1$ action.
