No, an email that has been permanently deleted from Gmail cannot be easily recovered by authorities — at least not in a straightforward or simple way. Once you delete an email and it's removed from the "Trash" folder (or if you've already emptied the Trash), it’s no longer visible to you or to anyone else who might have access to your account.

However, depending on how long ago the email was deleted and whether Google keeps backups of your data, there may be a way for authorities — such as law enforcement — to recover it through special means like a court order or a data request from Google. But this is not something that can be done easily by just anyone.

So, while it might be possible for authorities to recover the email, it's not something they can do "easily" in most cases.