There are 87 affordable units available by lottery at the two rental towers at 400 W. 113th St., at Amsterdam Avenue, including studios, one-bedroom and two bedroom apartments.
Twenty-seven studios at the development are available for $867 for one person making between $29,726 and $36,300.
Forty one-bedroom apartments are available for $931 for one person making between $31,920 and $36,300, or two people making a combined income of $31,920 to $41,460.
Twenty two-bedroom units for $1,123 are available for two people whose combined income is between $38,503 and $41,460, for three people with a combined income of between $38,503 and $46,620, or for four people with a combined income of between $38,503 and $51,780.
The two towers, which are connected by a set of stairs, are filled with amenities, including a laundry room, a screening room, a game room, a roof deck, a terrace with a setup for barbecuing, a bike room, an art gallery, a fitness center and a parking garage.
Not all of the amenities are included in the rent. A spokeswoman for developer Brodsky Organization did not immediately return request for comment regarding which amenities required an additional fee.
The Brodsky Organization signed a 99-year lease for the north site of the cathedral's property to build the towers, which will help fund repairs to the aging Gothic Revival, church officials said.
Residents initially tried to fight the development, decrying the loss of views of the world-famous cathedral.
Under the housing lottery, Community Board 9 residents have preference for 50 percent of the affordable units. City employees have preference for 5 percent of the units.
Leasing for the market-rate apartments started in January, with a move-in date for all tenants in late winter or early spring, according to a spokeswoman for the Brodsky Organization.
The deadline to apply for an affordable unit is April 12, 2016.
Applicants can apply online or request an application via mail by sending a self-addressed envelope to Enclave at the Cathedral c/o Urban Associates, LLC., P.O. Box 4089, New York, NY 10023.