Complex Period Lattice

Period Map

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.

PeriodMapping(A, prec): ModAbVar, RngIntElt -> Map

The complex period mapping from the rational homology of the abelian variety \(A\) to \({\mathbb{C}}^d\), where \(d={\rm dim}A\), computed using \(prec\) terms of \(q\)-expansions.

Period Lattice

Periods(A, n): ModAbVar, RngIntElt -> SeqEnum

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).