Can you tell me how to receive notification only of a new form being submitted, without the data of the form being in the email?

I am not sure how you meant here. If you can provide us with more clarity on what you require, we will be able to provide you with the appropriate response and suggestions.

From what I got so far, it seems you only want to be alerted/notified of form submissions via the email but without any content/message on the email notice.

You can achieve this by simply editing the email and removing the message content.

User guide: How to Edit the Email Template for Notifications and Autoresponders

You can remove the content of the email message.

Example:

Let us know if you need further assistance.