For Justice Sotomayor, the new job will start with hearing the election-law case Citizens United v. Federal Election Commission. It concerns whether the government may limit the showing of a negative documentary about Hillary Rodham Clinton under the campaign finance laws, and it attracted only limited attention when it was first argued in March.

In an unusual move in June, though, the court set the case down for re-argument on Sept. 9, asking the parties to address the question of whether it should overrule a foundational decision about the regulation of corporate speech and part of a decision upholding the McCain-Feingold campaign finance law.

Erwin Chemerinsky, the dean of the law school at the University of California, Irvine, said Citizens United is “one of the most important First Amendment cases in years.”

“It has,” Mr. Chemerinsky added, “the potential for dramatically changing all federal, state and local elections if the court holds that corporations have a First Amendment right to contribute money to candidates.”

The docket is also studded with business cases, and the decisions in them will provide hints about how the court will treat disputes arising from economic legislation pushed through Congress by the Obama administration.

“The Supreme Court,” said Joseph A. Grundfest, a law professor at Stanford, “will likely issue important decisions defining the permissible level of punitive damages, the validity of business method patents, whether and when parallel conduct among competitors violates the antitrust laws, and statutes of limitations in securities fraud action. But who the heck knows how Justice Sotomayor will vote in any of these cases?”

A former prosecutor, district and appellate court judge, she has a more fully developed record on criminal issues. Her views are in some ways more conservative than those of Justice Souter, meaning that this is an area where her vote may make a difference.