Matrix generators for Weil representations

Let r be an odd prime and F a field containing a primitive rth root of unity. Then for all ≥ 1, there is a faithful representation f: Sp₂(r) → GLr⁽F) called the Weil representation. We provide explicit matrices generating Sp₂(r) in GLr⁽F), which we have implemented in Magma. We also describe such generators for the irreducible Weil representations of Sp₂(r), which are of degree (r^ ± 1)/2 and arise as irreducible constituents of the Weil representations.