After I e-file, what documents or forms do I need to send by mail?

if you owe you need to mail 1040-V with a check to the address indicated on TT filing instructions.

• Make your check or money order payable to “United States
Treasury.” Don’t send cash.
• Make sure your name and address appear on your check or
money order.
• Enter your daytime phone number and your SSN on your
check or money order. If you have an Individual Taxpayer
Identification Number (ITIN), enter it wherever your SSN is
requested. If you are filing a joint return, enter the SSN shown
first on your return. Also enter “2019 Form 1040,” “2019 Form
1040-SR,” or “2019 Form 1040-NR,” whichever is appropriate.
• To help us process your payment, enter the amount on the
right side of your check like this: $ XXX.XX. Don’t use dashes or
lines (for example, don’t enter “$ XXX—” or “$ XXX xx/100”).

you can pay electronically (online) following these instructions - if you do do not mail in 1040-V

Paying online is convenient, secure, and helps make sure we get
your payments on time. You can pay using either of the following
electronic payment methods. To pay your taxes online or for more
information, go to www.irs.gov/Payments.
IRS Direct Pay
Pay your taxes directly from your checking or savings account at
no cost to you. You receive instant confirmation that your
payment has been made, and you can schedule your payment up
to 30 days in advance.
Debit or Credit Card
The IRS doesn’t charge a fee for this service; the card
processors do. The authorized card processors and their phone
numbers are all on www.irs.gov/Payments.

if you owe for the state and pay by check make sure it's mailed to the state and not the IRS - follow TT filing instructions for the state

states also have a method to pay online at their depart of revenue website

since you e-filed there are no other forms that need to be mailed if you pay by check.