Sorry for you're loss. Use the DL number of the person listed as the taxpayer on the 1040. That would be the parent, not you.
Depending on how long it's been since they passed, do not be surprised if your e-file attempt is rejected with an error of "SSN LOCKED". That just means that whoever handle the final arrangements of the deceased did their job. So the IRS has locked their SSN to prevent fraudulent use. If that happens, then you have to print, sign and mail it to the IRS, along with the 1310.
