Please click on the following link and enter your information, which will give you the TurboTax Electronic Postmark date you e-filed and the date of when you return was accepted if it was accepted: https://turbotax.intuit.com/tax-tools/efile-status-lookup/
You can also log into your TurboTax Online account and receive the information as well once you log in it will open your Tax homepage where you will see your Federal return transmitted date and acceptance date.
