When Lyft went public last month, its first day of trading was strong, with its share price closing at $78.29. That's $6.29 higher than its preopen share price of $72. 

Then things took a turn. By day two, the ride-hailing company's share price fell to $69.01. It's been on a downhill slide ever since. As of Thursday's close, Lyft's share price was $58.36.

On Wednesday, investors filed two separate proposed class action lawsuits against Lyft, according to Bloomberg. They allege the company misrepresented its market position when it went public saying it dominated 39 percent of the ride-hailing market when it might actually be less. The cases were filed in San Francisco's state court where Lyft is headquartered.

Lyft was the first tech unicorn to go public in 2019, a year that's predicted to be full of Silicon Valley initial public offerings. Lyft rival Uber publicly filed with the US Securities and Exchange Commission last week for what could be the largest IPO in US history. In the days following Uber's filing, Lyft's stock dipped dramatically to an all-time low of $56.11 on Monday.

A Lyft spokeswoman declined to comment on the lawsuits.