If you have a paid membership to Ancestry.com, you can access the following New Mexico records for Spanish, Mexican and United States Territorial periods:
* New Mexico, U.S., Civil Records of New Spain, 1621-1821- These records organized by "Twitchell Numbers". These are original Spanish era records and are in Spanish.
* New Mexico, U.S., Land Records of New Spain, 1692-1846 - These are original Spanish and Mexican documents as well as transcriptions of those records and United States court documents relating to Spanish and Mexican Land Grants.
* New Mexico, U.S., Wills and Probate Records, 1801-1993 - As described in the title, these are United States wills and probate records. You can browse these records by county, including Socorro County.
There are many other records that can be found on Ancestry, but I find these are particularly useful for New Mexico genealogy.