Invariants of Modular Abelian Varieties

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After understanding algorithms for computing modular forms, one can focus on arithmetic information associated to them, particularly to the weight 2 cusp forms for $\Gamma_0(N)$ . These correspond to isogeny classes of abelian varieties over $\mathbb{Q}$ which are factors of the Jacobian $J_0(N)$ . In weight 2 one can look at the invariants of a particular representative modular abelian variety, rather than the more abstract notion of a Galois representation.

The goal of this project is to develop algorithms and implementations to investigate as many as possible of the following invariants for general modular abelian varieties.

Half of this chapter was written by David Kohel.