Let A be a modular abelian variety. The period mapping of A is a map from the rational homology of A to a complex vector space.
The complex period mapping from the rational homology of the abelian variety A to Cd, where d=(dim)A, computed using prec terms of q-expansions.
Given an abelian variety A and an integer n return generators for the complex period lattice of A, computed using n terms of q-expansions. We use the map from A to a modular symbols abelian variety to define the period mapping (so this map must be injective).