If Gmail has not deleted the messages from the server, you can recover deleted emails after deleting them from your trash folder. You must open your gmail then click the drop down arrow on the left from your search box at the top of the screen. it will then ask you several question such as to: or from, subject, key words or date within. Click on the blue search button on the bottom left of the search box and all of your deleted emails will be revealed.
Gmail has two layers of deleting emails - deleting them as you see them from your inbox or folders, for example, and permanently removing them from the server. If you've simply hit delete or swiped to delete or archive them, it's pretty likely they'll still be residing in the trash rather than hanging out in the digital equivalent of email heaven (or hell).
Thankfully the search function in Gmail, used to discover old emails in your inbox, also works with the Trash folder. All you have to do is click on the Trash folder to access your deleted messages, then click on the search bar at the top and type in the keywords you think your email may have contained. Gmail will then present you with all the messages containing your search terms which speeds up the process of finding the email you're searching for.