The original Left Alliance was like that, but the current party has very little to do with that heritage. The younger generation started a slow coup in the late 90s and eventually pivoted the party to a completely new direction. In the process, they lost many of their old supporters. The left-wing conservatives who had traditionally voted communists didn't really feel at home in a party of liberal environmentalists.
> The left-wing conservatives who had traditionally voted communists...
As a person with US-oriented political definitions, I find that phrase almost impossible to parse. I can put "left-wing" and "traditionally voted communist" together, but in what sense are they "conservatives"?
I'm not saying that you're wrong. I'm just saying that I don't understand how the terms are used over there.
Economically hard left, socially conservative. There are often no good English terms for political positions that never existed as mainstream options in English-speaking countries.