Can I use 2×6 rafters for my garage roof?

I plan to build a 24ft x 30ft garage (28ft x 34ft with 2ft overhangs). I was planning on using 2×8 rafters, but I'm wondering if I can get away with using 2×6 rafters instead. The rafters are 24 inches on center and supported by two structural beams (LVL) spaced at 8 feet from the outside walls.

The beams are running the 30 foot length, supported by one column in the center of each beam (15ft from the outside walls) and obviously the beams also being supported by the outside walls.

The rafters will run the 28ft length spanning a 2ft overhang supported by the outside wall continuing 8ft to the first beam, then continuing another 8ft supported by the second beam, then another 8ft supported by the outside wall, and then a final 2ft for the overhang.

I was wondering if this can be done within current building codes first and secondly would the have a sufficient Load strength? I am in Northern New York for climate info. I know 2×8 rafters or even 2×10 rafters would be just fine but since I'm only actually spanning 8ft with the rafters could 2x6s be used for cost reduction purposes?