First of all congrats on the promotion.
I would ease the authority in gradually. When people step out of line, try to make an example (but not in a bad way) of the person least likely to start gossiping behind your back (i.e the quiet one). Then step it up from there.
I would try to keep it comfortable/fun but a line needs to be drawn that nobody should step over.
These people know they were getting away with a lot before. Try to make it clear that its your ass on the line and if your manager comes down on you like a ton of bricks, then you'll be returning the favour.
Personally I prefer a strict manager where you always know where you stand, to inconsistent laid back manager. But theres no reason why can't find a middle ground if you think that works best.