Is the trunk of your car your private space?

....depends upon the definition → of "private". If your car is owned by you personally, then yes, as part of the car, it is private space, but if the police want "to search your car", the the trunk is part of your car, and they will search it.

If you want to store items in the trunk so that they are hidden from view, but you have an SUV type vehicle, your "trunk" is essentially glass, so it will not be "private".