You can change your email notification settings in settings.
Click on the star washer near the top right corner: Then near the bottom of the right hand panel that appears choose the option that say Mail
Now a left hand panel appears. Expand your choices if necessary until you can see the option that says Mail\Automatic processing\Message. click on Message Options:
The three choices here are pretty self explanatory:
Play a sounds when items arrive
Display a notification when a new email message arrives
Empty the Deleted Items folder when I sign out
Turn on the notifications that help you and turn off the ones that don’t. Dont’ forget to click Save above those choices to keep them. Clicking the back arrow next to Options at the top of the left column brings you back to your email. Clicking the star washer again makes the settings disappear.