How low do sharks swim below sea level?

It depends of the shark species.

The whale shark can go deeper than 2,000 meters; the greenland shark and its relative, the pacific sleeper shark can go even deeper, with a recorded video register from a submersible near the coast of Brazil at 2,770 meters deep.

The deepest record (so far) is the portuguese shark (Centroscymnus coelolepis), reported at 3,675 metres.