Can't point you to the law, sorry
But you might have to look a bit further out. 40 years ago, when I lived in New York State, having a loaded rifle or shotgun in a car was illegal. The only loaded firearm allowed was a handgun, and there were restrictions on that.
The law has been on the books for a long time, and would apply to NYC as well. There might be (and probably is) seperate law for NYC adding to the general state law, I can't speak to that.
All else being equal (and it almost never is) bigger bullets tend to work better.