Favorable vulnerability, you play precision, so partner's 1♠ call is 11-15. 3 hearts was intermediate, showing 11-14, usually with a 7 card suit, but sometimes 6 with a particularly good playing hand. Playing in a club game, matchpoints.
The 3♥ call probably will not be repeated at any of the other tables. Does that have any bearing on your thinking?
Edit: Just realized I had the vulnerability wrong in the OP, edited to favorable. Not sure how much difference it makes, though.

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1♠-(3♥)*-X-(p),
3♠-(p)-?
*3♥ is intermediate