Note: this tutorial works even if the UTM parameters are no longer present in the URL when the form is submitted.
Open the popup in the builder
Click on your form
In the left column, click on the + sign and select "Hidden field"
Add an ID, turn on the "Populate the field with user attributes" option, and select "UTM campaign" in the dropdown list.
Reproduce the same process for all the UTM parameters that you want to collect.