Question: What is an example of what states retain authority over?
Sentence: Though international relations including international treaties are primarily the responsibility of the federal level, the constituent states have certain limited powers in this area: in matters that affect them directly, the states defend their interests at the federal level through the Bundesrat (literally Federal Council, the upper house of the German Federal Parliament) and in areas where they have legislative authority they have limited powers to conclude international treaties "with the consent of the federal government".
Answer in sentence: no