Seatmap -- shows assigned seats and blocked seats. However, there may be those without seat assignments. BE or tour groups are just some of the reasons for not having seat assignments. Pre-selected seats are less common from some Asian destinations. Generally considered the poorest indicator of the flight load situation.

E+ seatmaps can be deceptive since Silver elites do not have access until check-in and some upgrades will come from E+.

Fare class inventory -- the highest fare class for the cabin of interest will show the number of seats UA is willing to sell in that cabin. It caps at 9. UA will oversell economy if space exists in the premium cabin. UA generally does not oversell the premium cabin (but there have been reports UA may be testing the waters with 1? seat oversells in some markets).

Best to look at just the single segment's fare class inventory, as multi-segment listing may be the worst case of any segment.

Flight status -- will tell you the number of premium cabin seats sold and can show seats blocked due to overselling economy.

IMO Flight status is the best indicator for the premium cabin but with UA sometimes blocking seats on certain aircraft for crew rest or mobility/medical needs that do get release closer to departure, much of this is a black art.