  Geometric modularity has recently been conjectured to be a characteristic
feature for flux vacua with $W=0$. This paper provides support for the
conjecture by computing motivic modular forms in a direct way for several
string compactifications for which such vacua are known to exist. The analysis
of some Calabi-Yau manifolds which do not admit supersymmetric flux vacua shows
that the reverse of the conjecture does not hold.
