# 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).