[SalesForce] Insert trigger on Account creates new case and After Trigger on Case failed to Update case

I have created after insert trigger on Account which creates a new case when an account is created, I have created another after trigger on case and I am trying to update the field value or set any field in the case. While trying so I am getting the error:

Error: Invalid Data. Review all error messages below to
correct your data. Apex trigger AccountTrigger caused an unexpected
exception, contact your administrator: AccountTrigger: execution of
AfterInsert caused by: System.DmlException: Insert failed. First
exception on row 0; first error: CANNOT_INSERT_UPDATE_ACTIVATE_ENTITY,
caseTrigger: execution of AfterInsert caused by:
System.FinalException: Record is read-only Trigger.caseTrigger: line
4, column 1: []: Trigger.AccountTrigger: line 7, column 1.

Can u please let me know the reason ! Thanking in Advance

Trigger on Account:

trigger AccountTrigger on  Account(after insert) {
    for (Account cc : trigger.new){
        Case contactCase = new Case();
        contactCase.priority = 'Ultra High';
        contactCase.subject = 'Send them a free T shirt';
        contactCase.AccountId= cc.id;
        insert contactCase;
    }
}

Trigger on Case:

trigger caseTrigger on Case (after insert) {
    for ( Case c :  Trigger.new){
        if (c.SuppliedCompany== NULL){
        c.SuppliedCompany ='this is my new company';
        }
    }
}