N.M. Stat. § 73-10-28
The secretary of the board of directors shall cause notice of the filing of such petition to be given and published once each week for three successive weeks in a newspaper published in the county where the office of said board is situate, which notice shall state the filing of such petition and the names of the petitioners; a description of the lands mentioned in the petition, and the prayer of said petitioners; giving notice to all persons interested, to appear at the office of said board at a time named in said notice, and to show cause, in writing, if any they have, why the petition should not be granted. The time specified in the notice at which it shall be required to show cause shall be the regular meeting of the board next after the expiration of the time for the publication of the notice. The petitioner or petitioners, shall advance to the secretary sufficient money to pay the estimated cost of all proceedings under such petition before the secretary shall be required to give such notice.
NMS § 73-10-28