  We study the limit of Calabi-Yau modular forms, and in particular, those
resulting in classical modular forms. We then study two parameter families of
elliptically fibred Calabi-Yau fourfolds and describe the modular forms arising
from the degeneracy loci. In the case of elliptically fibred Calabi-Yau
threefolds our approach gives a mathematical proof of many observations about
modularity properties of topological string amplitudes starting with the work
of Candelas, Font, Katz and Morrison. In the case of Calabi-Yau fourfolds we
derive new identities not computed before.
