The Supreme Court declined yesterday to review the conviction of Patricia Hearst for the armed robbery of a bank, an action that makes the 24-year-old heiress to a newspaper fortune eligible to be put behind bars again.

Hearst was kidnapped in February 1974 by an organization calling itself the Symbionese Liberation Army. Two months later, after issuing a tape-recorded communique in which she said she had adopted the ways of the captors, she participated with SLA members in the robbery of a branch of the Hibernia Bank in San Francisco.

Police arrested her in September 1975. At her eight-week trial she said the SLA had coerced her into joining in the robbery, in which she carried an automatic weapon. A jury decided she had acted voluntarily.

She is under two concurrent sentences - seven years for armed bank robbery and two years for using a firearm to commit a felony.

At the time the sentences were imposed in September 1976 she had been in custody for a year. She was in jail two months longer before being freed - on $1 million bond - in November 1976. She would be eligible for parole after 14 more months in prison.

But her lawyer indicated they will ask U.S. District Court Judge William H. Orrick in San Francisco to shorten her sentence so that she would have to serve no additional time.

Orrick won't be formally notified of the Supreme Court's action for about 10 days. After that, he can hear a motion to shorten the sentence. He also can order her to prison.

Hearst's attorneys may also ask the Supreme Court to reconsider its decision not to review the case. The court rarely grants such requests.

In San Francisco the convicted woman's father, Randolph A. Hearst, chairman of the Hearst Corp. and president of the San Francisco Examiner, telephoned the newspaper to say the family would have no statement.

Pending formal notification of Orrick, Hearst remains free to live as she has for 17 months - travelling in California, visiting the family estate at San Simeon and shopping near her parent's home in the San Francisco suburb of Hillsborough, where she has spent much time

Because of threats on her life, her family retained a private security company to keep her under constant guard. Late last year, Bernard Shaw, 30, a San Francisco policeman working off-duty as her bodyguard, was romantically link with Hearst, United Press International said. Her purse, containing $400, was stolen from his van while it was parked outside his home.

Former U.S. Attorney James Browning Jr., who prosecuted the case for the government, said he was "very happy" that the Supreme Court agreed with what he has said for some time: "that she received a fair trial and there was no error."

In contrast, her lawyers contended in a brief in the Supreme Court that the late Judge Oliver J. Carter had made numerous errors that denied Hearst a fair trial.

They asked the justices to overturn a ruling by the 9th U.S. Circuit Court of Appeals last November that she had raised "no novel issues."

The lawyers raised essentially the same arguments in the Supreme Court, which rejected them without comment. Justice William J. Brennan Jr. rated two of the issues worthy of a hearing, but review is granted only if four of the nine justices vote to do so.