Legal Question in Civil Rights Law in New Mexico

No. Although it is theoretically possible to get that right restored in New Mexico, it is never possible to have it restored under federal law. Once you have been convicted of a felony, you become a "prohibited person" under federal law, for life, and may not legally possess a firearm, ammunition or a destructive device ever again. The penalties for "felon in possession" are severe and not worth the risk. The only way around this is a presidential pardon, and the chances of obtaining one of those are slim and none.