Domestically, first letter of fare basis code only matches booking class for main cabin coach fares. For BE, domestic PE and FC fares, first letter from fare basis code is a coach fare class and does not match the booking class. There is a dual inventory check for such fares (must be both coach inventory in the first letter of the fare basis code, and inventory in the booking class of the fare). PE fares can be identified by second to last character of the fare basis code as it will be an 'I' or an 'O'. Coach fares have an 'E', Basic Economy have a 'B', and FC will have a 'P'. If you have an ExpertFlyer account, you can lookup the booking class by selecting the routing rules for a fare by it's fare basis code (under the BK column).

Edit to add, I guess I forgot 'B' fares are actually Economy Plus on UA domestically (I in second to last character of fare basis code). Similar to how DL sells it's Comfort Plus cabin as separate fares (W and S booking classes).