Does any body knows any low income apartments in Manhattan ?

ok i am 21 years old and i am still living at home with my mother. . And my two younger siblings. and i have a job but i only have a part time job .at home depot which i get paid 8.55 per hour. and i wanna move out my mothers house and move to Manhattan because all my life i lived in brooklyn i i just wanna move out of brooklyn to Manhattan does any body knows any low income apartments in Manhattan that would go by my income or not ?