Greece inaugurated its first leftist-led government on Monday, also ushering in the first anti-austerity party to lead a eurozone country.

Just five years ago, Syriza was a small party with little clout. But the party, and its charismatic young leader, Alexis Tsipras, who is now the new prime minister, rode public anger against a multi-billion euro bailout that came with draconian spending cuts and tax hikes.

Those austerity measures ravaged the economy, turning a recession into a full-blown depression. The country lost a quarter of its economic output. More than 25 percent of Greeks are unemployed. Half of families live at or near the poverty line.

Panagiota Kontogianni, a public sector worker, says she understands why people voted for Syriza even if there were signs that the Greek economy was turning around. There was a primary surplus, a projection that the economy would return to growth this year.

She voted for New Democracy, the conservative party that had led a coalition government since 2012. She said she wanted stability. But others around her had lost hope, she says. "You don't have [enough] to eat, or you don't have electricity," she told DW. "You can hold on for how long. One month? One year? Two years? They have lost their patience."

Electra Kanellou, an archaeologist, says she spent the last four years feeling uneasy about the future. "I'm always living in fear that something will happen, and I will lose my job, and then maybe I have to move out of Greece," she sys. "I think that's the main thing, fear. I'm always afraid of something."

She voted for Syriza because the party promises to restore power to people, not banks. She says Greece has lost its sovereignty to foreign lenders since the 2010 bailout.

'Out with the troika'

But Jens Bastian, a German economist based in Athens, says the new Syriza-led government must still negotiate with those lenders, whom Greeks call the troika. They represent the European Union, the European Central Bank and the International Monetary Fund.

Many newly-elected Syriza parliamentarians have declared that they will "kick out the troika."

"Well, it is rather challenging statement to make," Bastian says. "It begs the question: if you will not negotiate with the troika, does that mean the troika is persona non grata in Athens? If the answer to that question is yes, and various representatives of Syriza give that answer, then the follow-up question is: Okay, are you then going to negotiate? Who is your negotiating partner? Who is sitting on the other side of the table? And who has the authority to enter into any solution or any grand bargain?"

Negotiating with Europe may be much harder now that Syriza, which failed to win an absolute majority in parliament, will govern with Independent Greeks, a right-wing nationalist party that has described the Germans as "occupiers," invoking the Nazis of World War II. The two parties appear to have little else in common but their opposition to austerity.

The alliance may unsettle European leftists, who were ecstatic over Syriza's win on Sunday night. Supporters of Podemos, the rising anti-austerity movement that's leading in public opinion polls in Spain, danced with Italian Communists and the Greeks to Cretan revolutionary songs.

But Syriza leaders are staying away, at least for now, from the ideological storm that's likely to ensue from this partnership. Instead, they're trying to focus on what needs to happen now, says Mathaios Tsimitakis, a reporter for Syriza's newspaper, Avgi.

"The biggest problem in Europe right now is deflation, and the reason why the [European Central Bank] decided to move to some type of quantitative easing in order to tackle this problem," Tsimitakis says.

Tsimitakis also predicts that European leaders will lessen Greece's giant debt load. "As it always happens in the European Union, a compromise will be reached," he says. "And a compromise in this case is not a compromise between Syriza and the European Central Bank. It's a compromise among 27 member-states, European institutions, and the new government in Greece. So what that compromise is going to look like, I really don't know. But I know there's a bottom line, the red lines, and the humanitarian crisis [here] is one of them."

'No one trusts politicians'

In his victory speech Sunday night, Tsipras promised to restore dignity and self-respect to Greeks, to help those impoverished by the crisis. He also promised to take on the country's oligarchs and crack down on endemic corruption in the state.

Ilias Panteleakos, a naval engineering student who leads Syriza's youth student, says that's a message that really moves young Greeks.

"One very important thing for us is to end this madness of corruption in Greece," Panteleakos says. "It's very important. We are a European country and the state is so corrupt that no one trusts the politicians, no one trusts the state mechanism, so one very important goal for Syriza is to stop this and build a new [relationship] between politicians, between the state and civilians.