  A number theoretic approach to string compactification is developed for
Calabi-Yau hypersurfaces in arbitrary dimensions. The motivic strategy involved
is illustrated by showing that the Hecke eigenforms derived from Galois group
orbits of the holomorphic two-form of a particular type of K3 surfaces can be
expressed in terms of modular forms constructed from the worldsheet theory. The
process of deriving string physics from spacetime geometry can be reversed,
allowing the construction of K3 surface geometry from the string characters of
the partition function. A general argument for K3 modularity follows from
mirror symmetry, in combination with the proof of the Shimura-Taniyama
conjecture.
