You are eligible for Mexican citizenship if you are born abroad to Mexican parents. However, you need to file paperwork with the Mexican consulate to gain your citizenship.

Those documents vary based on the context under which you’re applying for your citizenship. This list pertains to foreign born people who are applying for citizenship through parents who are Mexican citizens:

Your parents’ marriage or divorce certificate

Proof of at least one parent’s Mexican citizenship and both parents’ citizenships in general (regardless of country if one parent is not Mexican). Those documents include:

a. birth certificate
b. valid Mexican passport
c. national voter card

Your own birth certificate (long version). You’ll also need an apostille and a translated version of the document.

IDs for everyone involved in the process, including passports or driver's licenses, state identifications or school identifications.

Source: https://transferwise.com/gb/blog/how-to-get-citizenship-in-mexico