ALEXANDRIA, Va. — One month after a judge declared Google’s search engine an illegal monopoly, the tech giant faces another antitrust lawsuit that threatens to break up the company, this time over its advertising technology.

The Justice Department, joined by a coalition of states, and Google each made opening statements Monday to a federal judge who will decide whether Google holds a monopoly over online advertising technology.

The regulators contend that Google built, acquired and maintains a monopoly over the technology that matches online publishers to advertisers. Dominance over the software on both the buy side and the sell side of the transaction enables Google to keep as much as 36 cents on the dollar when it brokers sales between publishers and advertisers, the government contends.

Regulators allege that Google also controls the ad exchange market, which matches the buy side to the sell side.

Justice Department lawyer Julia Tarver Wood said during her opening statement, “One monopoly is bad enough. But a trifecta of monopolies is what we have here.”

Google says the government’s case is based on an internet of yesteryear, when desktop computers ruled and internet users carefully typed precise World Wide Web addresses into URL fields. Advertisers now are more likely to turn to social media companies like TikTok or streaming TV services like Peacock to reach audiences.

In her opening statement, Google lawyer Karen Dunn said Supreme Court precedents warn judges about “the serious risk of error or unintended consequences” when dealing with rapidly emerging technology and considering whether antitrust law requires intervention. She also warned that any action taken against Google won’t benefit small businesses but will simply allow other tech behemoths like Amazon, Microsoft and TikTok to fill the void.

According to Google’s annual reports, revenue has declined in recent years for Google Networks, the division of the tech giant that includes such services as AdSense and Google Ad Manager that are at the heart of the case, from $31.7 billion in 2021 to $31.3 billion in 2023.

The trial that began Monday in Alexandria, Virginia, was initially going to be a jury trial, but Google maneuvered to force a bench trial, writing a check to the federal government for more than $2 million to make moot the only claim brought by the government that required a jury.

The Virginia case comes after a major defeat for Google over its search engine, which generates most of the company’s $307 billion in annual revenue. A judge in D.C. declared the search engine a monopoly, maintained in part by tens of billions of dollars Google pays each year to companies like Apple to lock in Google as the default search engine presented to consumers when they buy iPhones and other gadgets.

And in December, a judge declared Google’s Android app store a monopoly in a case brought by a private gaming company.

In the search engine case, the judge has not yet imposed any remedies, nor has the government offered its proposed sanctions.