In official documentation you can find the info:
Each push notification includes a payload. The payload contains
information about how the system should alert the user as well as any
custom data you provide. The maximum size allowed for a notification
payload is 256 bytes; Apple Push Notification Service refuses any
notification that exceeds this limit.
Apple has already updated the documentation. The 2KB for the maximum payload size is just for devices running iOS 8. The official doc says:
In iOS 8 and later, the maximum size allowed for a notification payload is 2 kilobytes; Apple Push Notification service refuses any notification that exceeds this limit. (Prior to iOS 8 and in OS X, the maximum payload size is 256 bytes.)