The land upon which any building, improvement or structure is constructed, together with a convenient space about the same, or so much as may be required for the convenient use and occupation thereof, to be determined by the court on rendering judgment, is also subject to the lien, if at the commencement of the work, or of the furnishing the materials for the same, the land belonged to the person who caused said building, improvement or structure to be constructed, altered or repaired, but if such person owned less than a fee simple estate in such land, then only his interest therein is subject to such lien.
NMS § 48-2-4