When António Costa, a prime minister well liked by European leaders, handily won his third term as prime minister in 2022, many Portuguese prepared for a lasting, stable government given his Socialist Party’s strong majority in Parliament.

But by late last year, Mr. Costa had resigned, his government embroiled in a corruption investigation involving lithium exploration concessions.

On Sunday, Portugal faces a new election. It has raised the prospect that the Socialist Party could lose power for the first time in more than eight years, as well as the possibility of an unstable minority government.

One of the most significant changes in the election campaign has been the rise of a hard-right populist party.

What set off the vote?

Mr. Costa resigned in November after the opening of a corruption investigation into lithium exploration concessions, hydrogen production and the construction of a data center.

Lithium is key to helping the European Union transition to clean energy, and the bloc mostly relies on imports.

In Portugal, the lithium explorations were contentious even before the investigation into the awarding of concessions and had faced public opposition for the environmental damage the mines could cause.

The investigation now threatens to dampen much-needed foreign investment, said Marina Costa Lobo, a political scientist at the University of Lisbon. “And this might be problematic for Portugal,” she added.

Mr. Costa has not been formally charged with any crimes.

In televised remarks in November, he said that “no illicit act weighs on my conscience,” but added that the “dignity” of the prime minister’s office was incompatible with suspicions swirling around it.

Who is running now?

Portugal is electing a new Parliament in the early general election. The Socialist Party is in a tight race with the Democratic Alliance, a coalition of center-right parties led by the Social Democratic Party.

The Socialists are expected to win about 28 percent of the vote, according to an aggregation of polls by Politico, and the Democratic Alliance about 33 percent.

Pedro Nuno Santos, backed by the Socialist Party’s left wing, succeeded Mr. Costa as the head of the party.

Members of the Social Democratic Party have also been affected by corruption inquiries, with the president of a local government recently resigning.

Most surprising has been the rise of Chega, a populist right-wing party. Even though Chega is trailing behind the two mainstream parties, according to an aggregation of polls by Politico, a strong showing in the election could turn Chega into a kingmaker if no others can secure an outright majority.

Luís Montenegro, the Social Democratic Party leader, has ruled out making a coalition with Chega. Chega has made harsher punishment for corruption a pillar of its campaign, with billboards that read: “Portugal needs a cleanup.”

If his party comes first, Mr. Montenegro could form a minority government, a potentially unstable outcome that might not last very long, according to experts.

How popular is the far right?

Unlike other European countries, Portugal for years had not seen hard-right, anti-establishment parties gain traction among voters.

The rise of Chega, which means “enough” in Portuguese, is changing that, and a strong showing in the election could spell the end of the country’s exception.

“For us here in Portugal, it would be a novelty,” said José Santana Pereira, an associate professor of political science at the University Institute of Lisbon.

The party, founded in 2019, received about 1 percent of the vote in the 2019 election. That rose to about 7 percent in 2022, and the party is now predicted to win 16 percent of the vote, according to an aggregation of polls by Politico.

What are the main issues at stake?

Despite the corruption investigation, and Chega’s insistence upon it in its campaign, many voters seemed most preoccupied with issues affecting their everyday lives, Ms. Costa Lobo said.

With persistently low wages not keeping up with inflation, the Portuguese seem mostly preoccupied with the cost-of-living crisis. House prices have doubled in the past eight years, partly because of tourism rentals, making property unaffordable especially to the younger generations.

“Housing has become one of the main issues in the election,” Ms. Costa Lobo said. “Middle-class citizens are no longer able to rent or buy.”