JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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Sub-accounts can indeed create new forms. As long as the form is created in the folder that was shared with them by the upgraded account, the forms will have the upgraded limits. If the sub-account is missing the functionality to create them, have them go into their account settings and upgrade their account to a Free/Starter account:
This should give them full functionality.
If you have any further questions, let us know and we will be happy to help.