Where is the train station parking for "hamlet" East Garden City residents?

Hi, I just moved to East Garden City and I take the Garden City train on the Hempstead Line, I need to park in the train station parking lot but you need a sticker. I tried to get the sticker and they said that East Garden City is not part of Garden City that its one of the hamlets cities of the Town of Hempstead. So where do we belong to? Where can I take the train, which line and be able to park my car there? Thank you!