How to turn on email alerts on iPhone 5s/iOS7?

Here is what I currently have one:
Notification Cenre > Mail > Alerts ON. Sound > On as 'Note'
Show in notif centre > ON
Show on lock screen > ON

Sounds > New Mail > ON as Note

Mail, contacts, calendars > Fetch new data > PUSH

Why isn't it working? Aghhhhhh

Added (1). I use gmail btw

I know Gmail has some problem with ios. ( fetching mail, notifications and deleting. ) i recommend like the same to my girlfriend too to use their own app for best result.

You can delete the account and re apply the account maybe this will solve the problem.

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