The rules depend on which Shinkansen route you are taking. The usual route is between Tokyo and Kyoto/Osaka and you will book with JR Central and they have a
specific guide (
https://global.jr-central.co.jp/en/i...sized-baggage/) you can follow. Basically behind the last row seats of each car in the direction of train travel are for the oversized luggages (oversized luggage area). There are also oversized luggage compartments reserved for another two seats in the same car. Hope that helps.