With regard to the battery being new, keep in mind that batteries can come defective from the factory and even a good battery can be ruined in a day with miss-use. So really, "new" means next to nothing.
If you intend to use the battery without shore power, you really need a true "deep cycle" battery. The most common batteries installed in trailers are Marine/Starting (aka combo) batteries. You can tell it's not a true deep cycle if it includes Cold Cranking Amps (CCA) on the label.
If you plugged into shore power, the converter in the trailer should be charging the battery, but this assumes the converter is working. With the trailer plugged into shore power, check the voltage across the battery posts. If it is 13v+, then the converter is working and the battery should be charging.
If you want to use the battery at times when shore power is not available, there is a large learning curve to the care and feeding of coach batteries. If this is you intent, start asking questions
There's a lot to learn.