No . notification settings there?
Open Gmail app, tap the menu button upper left of screen, scroll down to settings, you should see general settings and under that your Gmail account address, tap your email address, tap on Inbox sound & vibrate - on the resulting screen tap Sound. That will take you to your list of notification tones, at or near the top you should see one that says "silent" choose that one and then you shouldn't hear any more notifications from Gmail.