Am I eligible to get unemployment.?

I was at a part time job. I asked for more hours, and was denied. I went to find a new job while still working at the old one; I found a new one and was promised full time. I put in my 2 weeks notice at the old job and left on good terms(they understood I was quiting for more hours). Well, at the new job I've been working nearly a month and am still getting less hours than the old one. Can I quit and still get unemployment?