Does the property have the right to take back the parking space without a contract parking space, if the parking space has expired and the parking fee has not been paid?

No, the property management company is just a service organization, and there is no driving right of laws and regulations. As a property service provider, property companies should provide corresponding services for owners, including parking space rental services. If the owner fails to pay the parking fee on time, the property management company should take a legal and reasonable way to demand payment, instead of directly recovering the parking space. Therefore, there is no contract for parking spaces, and there is no contract for parking spaces. The property has no right to recover parking spaces without paying parking fees.