  In the context of studying the 4D effective potentials of type IIB
non-geometric flux compactifications, this article has a twofold goal. First,
we present a modular invariant symplectic rearrangement of the tree level
non-geometric scalar potential arising from a flux superpotential which
includes the S-dual pairs of non-geometric fluxes $(Q, P)$, the standard NS-NS
and RR three-form fluxes $(F_3, H_3)$ and the geometric flux ($\omega$). This
`symplectic formulation' is valid for arbitrary numbers of K\"ahler moduli, and
the complex structure moduli which are implicitly encoded in a set of
symplectic matrices.
  In the second part, we further explicitly rewrite all the symplectic
ingredients in terms of saxionic and axionic components of the complex
structure moduli. The same leads to a compact form of the generic scalar
potential being explicitly written out in terms of all the real moduli/axions.
Moreover, the final form of the scalar potential needs only the knowledge of
some topological data (such as hodge numbers and the triple intersection
numbers) of the compactifying (CY) threefolds and their respective mirrors.
Finally, we demonstrate how the same is equivalent to say that, for a given
concrete example, various pieces of the scalar potential can be directly read
off from our generic proposal, without the need of starting from the K\"ahler-
and super-potentials.
