Hundreds of families have submitted early-bird applications to the newest charter school in Eva Moskowitz’s chain, which so far lacks a home but has seen no shortage of controversy.

Upper West Success Academy reports that 357 families have filed applications since the school was approved last month. Two-thirds live in District 3, the diverse and relatively wealthy district stretching from 59th Street to 122nd Street on the West Side of Manhattan where the school will be located.

“Given that every great elementary school on the Upper West Side is overcrowded and the terrific private schools cost more than $30,000 a year, it’s hardly surprising that Upper West Side parents are lining up for a high performing charter school,” Moskowitz said in a statement. Her organization is also touting the results of a phone poll that found 70 percent of neighborhood parents would support the school opening in the area. When told that the school would share space with another public school, support dropped to 59 percent.

But applications from 269 district families and a poll of 300 households does not “demand” make, according to parent leaders who are pushing back against the school. They say the city would do better to invest in existing schools rather than to carve out space for a charter school.

Resistance from local parents is one reason why Upper West Success is still without a site. The city tried to place the school inside PS 145 on West 105th Street but backed down after the community protested. Now city officials say the school, which will start with a kindergarten and first grade, will likely open in the Brandeis High School building.

At the crux of the debate is the question of whether District 3 needs charter schools, which are meant to serve needy students and so far are mostly located in low-income neighborhoods. The district contains some of the highest-performing schools in the city and includes some of the most affluent zip codes. Moskowitz is billing Upper West Success as an alternative to tony private schools and arguing that middle-class parents need school choice just as much as poor families, a case she will press at a series of apartment parties starting next week.

“They want upper-middle-class white kids who, because the DOE is not paying attention to those schools, are going to be attracted to a school the DOE favors heavily,” said Noah Gotbaum, president of the district’s elected parent council.

But District 3 also serves many poor students and has some schools that enroll black and Hispanic students almost exclusively. It is home to a dozen elementary schools that scored a D or F on their most recent progress reports. Upper West Success plans to offer preference to children zoned for those schools, along with students with disabilities and those classified as English language learners.

Gotbaum said the numbers sound like the school’s aggressive marketing — he said he has received 18 pieces of mail from Upper West Success — isn’t paying off.

“If she doesn’t get thousands of applications, it will be shocking because of the millions of dollars she’s spending in saying there are no good options in the district,” he said.

But Upper West Success has more than four months to collect applications. Charter schools are required by law to accept applications at least until April 1, when they are first permitted to hold admissions lotteries.

Of the 357 current applicants, 14 percent live in Harlem, home to the first three Success Network schools. Another 10 percent live in the Bronx, where the network just opened a school this year.

Gotbaum said he plans to conduct his own survey of parents in the district.