To be “on the left” at minimum you need to be totally opposed to the capitalist system.

From there, there are many ideologies to choose from whether authoritarian (like Marxism-Leninism, Maoism, Stalinism, etc.) or anti-authoritarian: mutualism, communalism, one of the many strains of anarchism, etc.

Also if you’re authoritarian I’d say it’s questionable whether you’re still on the left.