Q. Am I a resident if I’m a student supporting myself?
A. No. It takes more than that.
The general rule is students are residents of their home state until they take concrete steps to change it. This is true whether they are a dependent or not.
Intent is a key element ("intend to stay in New York after school..... but I no longer consider (NM) my home state"). On the other hand. "I still have an NM state ID and am registered to vote in NM" indicates otherwise.
Bottom line: it's whatever you want it to be until you get audited. My opinion, based on your description, is that you are still a NM resident. The intent of an undergrad (you don't say what year you're in) to stay in NY is fairly limited.
