# Some modular abelian surfaces

## TL;DR

This paper constructs explicit examples of modular abelian surfaces over the rationals with controlled bad reduction primes, utilizing a significant recent theorem in the field.

## Contribution

It provides explicit examples of modular abelian surfaces with specified reduction properties, leveraging the main theorem of Boxer-Calegari-Gee-Pilloni.

## Key findings

- Explicit examples of modular abelian surfaces over Q
- Surfaces have good reduction outside 2, 3, 5, 7
- No extra endomorphisms on these surfaces

## Abstract

We use the main theorem of Boxer-Calegari-Gee-Pilloni (arXiv:1812.09269) to give explicit examples of modular abelian surfaces $A$ over $\mathbf{Q}$ without extra endomorhpisms such that $A$ has good reduction outside the primes 2, 3, 5, and 7.