Three powerhouse Boston law firms have joined forces and are suing the state on behalf of students who were denied a spot in city charter schools.

The pro bono suit asserts that the demand for charter school seats exceeds the supply in Boston because of “an artificial legal cap” -- and is demanding that cap be lifted.

The charter schools are open to all students in the city, but there are lotteries that determine which students are admitted. 

The suit by the three firms -- WilmerHale, Goodwin Procter and Foley Hoag -- says thousands of students were unable to secure a seat last year through the schools’ lotteries.

Many, the lawyers group said Sunday,“find themselves trapped in a failing non-charter public school.”

“Every student in Boston has a right to an adequate education, yet thousands of students are unfairly denied that right every year by the artificial limits placed on public charter schools operating in the city,” said William Lee, a partner at WilmerHale. “As a result, these students are often forced to attend schools where most students cannot read or do math at grade level.”

A spokesperson for the Massachusetts Department of Elementary and Secondary Education could not immediately be reached comment.