None at all, eh? Well, that's weird.
I receive notifications, and this is how mine is set up in Settings->Notifications->Email:
Notifications ON
App icon badges ON
Then, under my primary email account:
New emails ON
Make sound
Tap on "Make sound," and I see the following:
Importance: High: Make sound
Sound: Whisper
Vibrate: OFF
App icon badges: ON
On lock screen: Do not show notifications (I like them to show up in the notification shade only)
And I have the other categories set up identically to that (VIPs, Snooze, Privacy and security, Miscellaneous)