This coat looks ordinary on the outside but inside the coat are many different pockets. Each is linked to an extra dimensional space that varies in size depending on the opening of the pocket. 

Small - a space equivalent to a small pouch 

Medium - a space equivalent to a small sack 

Large - a space equivalent to a medium pocket on a bag 

The number of pockets is determined at DM discretion but will always have at least one large pocket that is big enough for a spell book, 1 medium pocket big enough for a few scrolls and 2 small pockets for components. The coat also has the ability that if a spell book is placed into the large pocket it will allow the wearer to ritually cast spell without having to have the spell book out