What kind for mailbox that you used? Exchange mailbox, Office 365 mailbox, Outlook.com or mailbox hosted on other mail server?
If you mailbox is full, you could delete some useless emails from your mailboxes, you can also contact your mail server administrator to increase your mailbox quota. If you using an Exchange mailbox, you could contact your administrator to check on your mailbox. If you are using Office 365 mailbox, you can ask your mail server administrator to contact Office 365 support.
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