just because the battery is new dont count it out!
you need a multi meter set to 12v DC and with engine running (no headlights or accessories) on check the voltage of the battery. no leaving the multi meter connected turn on your accessories (full beam, top speed heaters, fogs front and rear, heated screen) check multi meter again. normal charge is around 13.5 - 14v and the alternator should try to stay at this level, if its dropping below 12 - 11v alternator has a problem. turn everything off and check again should level itself at 13.5 - 14v again.
if everything is ok there, get yourself a side lamp bulb
bend the terminals so they point away from the bulb, with the engine off remove the negative terminal and bridge the gap with the bulb
bad drawing but hopefully you get the idea, if the bulb glows quite bright then you have a drain somewhere on your vehicle and that needs to be investigated if its so very very very dim or not at all thats fine