Unfortunately, our major Alberto Ruiz Gallardón thought that 18 € / day in a public parking was too cheap and this year he changed the prices. Now you have to pay 27 € / day
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I know a privately owned / operated parking at Augusto Figueroa street. They charge 19 € / day, though they don't take reservatons.
You can also try to arrange something with the private parking located at Farmacia street (15 € /day). They seem to be very busy and they are the cheapest one I know.