The new Gmail Android app is a great way of only getting notified about mail that’s actually important to you. However, you can decide which labels get the right to show you notifications. The option is kind of buried in Settings, but it’s useful and something you might want to set up.
Click the menu button on the top right side of the Gmail Android app, then tap Settings.
Now, select the e-mail account you want to edit.
Tap Inbox Sound.
Now you can cycle through your labels and choose whether you want a notification for them or not.