This filled out convention card for SAYC indicates that negative doubles are played through 2S. By this agreement (which could be amended by partnership agreement, but which invalidate the claim to be playing pure SAYC) the double of a 2S jump overcall is a Negative Double. This bid should indicate 4+ hearts and game invitational values (10+ points), and generally deny any particular strength in spades.
If the jump overcall were above the level of 2S, such as in the auction
1H - 3D - double,
it wold be a penalty double showing diamonds and suggesting the collection of a penalty against a 3D contract.