Dennis,
Please see the complete regulations for New Mexico listed in the Onl;ine Mining Guide tab next to the prospecting tab for any claim. The short answer is yes but you will need to contact the local ZBLM office and the state for any updated regulations. New Mexico is one state that has done an excellent job in keeping us informed of regs but I have not received any updated from them since the pandemic started. you cah find the NM regs by following this link. https://www.goldprospectors.org/testpage/GPAAClaimDirectory/Property-Profile/ClaimId/131/ctab/Regulations#.X6xLnMhKiUk
I will always advise you to check with any area's current regs prior to going out to assure that you are in compliance with not only Federal regulations but any additions to State regs as well.
Hope this helped.

Kevin