Email storage on a cPanel server is governed by the allocated disk space for email accounts created from within the cPanel interface.
If you have access to cPanel for your account, you can find the allocated disk quota for your email address and other email accounts by going to cPanel > Email Accounts.
Clicking on the Manage button in front of a user’s email address takes you to the Manage an Email Account page where you will find the account’s Allocated Storage Space under the Storage heading.
Allocated Storage Space when assigned to an email account is the amount of space that an email account can use to store emails. Interestingly you can specify storage space in Megabytes, Gigabytes, Terabytes and even Petabytes! There’s also an ‘Unlimited’ option to help you avoid the hassle and use as much disk space allocated to your cPanel account.
If you are an end user with an email address like [user]@domain.tld you may contact your email administrator or account owner who can check your mailbox’s quota.