Those overhead racks are the only storage space for luggage on the bullet-trains. The Japanese travel light – small overnight bags. Some tourists end up nursing large suitcases on their lap. Smart tourists use one of the baggage delivery companies to get their luggage sent ahead (at very reasonable cost) to their hotel in the destination town.
The rearmost seat in every carriage has a small space behind it in which you can put a suitcase but you must pre-book that seat and the luggage.
Japan Tourist Tips 