WASHINGTON — A former Boston University student who was ordered to pay $675,000 for illegally downloading and sharing 30 songs on the Internet says he will continue fighting the penalty, despite the Supreme Court’s refusal Monday to hear his appeal.

Joel Tenenbaum, 28, of Providence, R.I., said he’s hoping a federal judge will reduce the amount.

“I can’t believe the system would uphold a six-figure damages amount for downloading 30 songs on a file-sharing system that everybody used,” Tenenbaum said. “I can’t believe the court would uphold something that ludicrous.”

A jury in 2009 ordered Tenenbaum to pay $675,000, or $22,500 per song, after the Recording Industry Association of America sued him on behalf of four record labels, including Sony BMG Music Entertainment and Warner Brothers Records Inc. A federal judge called the penalty unconstitutionally excessive and reduced the award to $67,500, but the 1st U.S. Circuit Court of Appeals later reinstated it.

The 1st Circuit said a new judge assigned to the case could reduce the award again, but the record labels would then be entitled to a new trial.

Tenenbaum, who said he just graduated Sunday from the university with a doctorate in statistical physics, said he doesn’t have the money to pay the judgment.

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“I’ve been working on a graduate student’s stipend for six years now and I have no such money,” he said.

Tenenbaum argued that the U.S. Copyright Act is unconstitutional and that Congress did not intend the law to impose liability or damages when the copyright infringements amount to “consumer copying.”

During the trial, Tenenbaum admitted he downloaded and shared hundreds of songs by Green Day, Nirvana, The Smashing Pumpkins and others. His lawyer suggested the damages should be as little as 99 cents per song, about the same amount Tenenbaum would have to pay for a legal online song purchase.

Lawyers for the recording industry argued that illegal downloading hurt the recording industry by reducing income and profits. A lawyer for the recording labels described Tenenbaum as a “hardcore” copyright infringer. The association said it offered to settle the case for $5,000 early on, but Tenenbaum declined.

“We’re pleased with this decision,” RIAA spokeswoman Cara Duckworth said after the Supreme Court’s announcement Monday.

In the only other music-downloading case against an individual to go to trial, a judge last year reduced the penalty imposed on a Minnesota woman from $1.5 million to $54,000. An appeals court has scheduled arguments for next month in the case of Jammie Thomas-Rasset.