Per 5e rules, you would get higher level spell slots, but not higher level spells. You could upcast a 1st or 2nd level spell, but not learn a 3rd level spell.
Ah, but what about wizards learning higher level spells from scrolls?
Per 5e rules:
"When you find a wizard spell of 1st level or higher, you can add it to your spellbook
if it is of a spell level you can prepare and if you can spare the time to decipher and copy it."
"You determine what spells you know and can
prepare for each class individually, as if you were a single-classed member of that class."
