If the left turn arrow signal is red it does not matter that the straight traffic lanes on your side of the road have a green light. Turning left on a red arrow light is similar to going straight through a red light. There are a few state statute sections that you might have been cited for according to your description of your ticket. 

If you were written up for failure to observe a traffic signal, state statute section number 39:4-80, this is a 2 point moving violation in NJ. If the ticket was for statute section 39:4-105, failure to stop for traffic light, it would also be a 2 point offense.

Instead if you were written up for making an improper turn at a traffic light, number 39:4-115, it is a 3 point traffic violation. A citation for an improper right or left turn, 39:4-123, is also worth 3 DMV points on your NJ driving record.

If the NJ state statute you were ticketed for was not listed here you can contact the New Jersey Motor Vehicle Commission (MVC) to find out how many points will be assigned to this violation if you are convicted of it.