Judgement states for a total judgment of $ 4574.00 WITHOUT COSTS. HOW MUCH DO I OWE?

If the judgment was signed by the judge then you owe 4,574.00. It is unlikely that the court will order additional amounts but it depends of the context. You may want to consult with a landlord-tenant attorney in order to evaluate the specifics of your case.

Dear Glen Cove Tenant:
Do you mean that you were sued in a nonpayment case, and the landlord's attorney told you to go home, and then in your absence, the landlord requested a default judgment? Did you owe any rent at all to the landlord?
If so, you need a lawyer, now.

According to the judge, you owe $4574.