You're better off abstracting the common functionality of the
Display_Mode class into an abstract base class or interface and then defining each individual mode as a class that inherits from the base class (or implements the interface).
These specialised mode classes would then explicitly define the parameters they require in their constructors and/or methods, and would be responsible for producing the output that each "mode" requires.
It's difficult to give more specific advice than this without knowing exactly what your
Display_Mode class is supposed to do, however.
The idea here is that you should avoid do-it-all classes in OOP, preferring small, self-contained classes each with a single purpose. By giving each mode its own class that can independently render its content, you're making it easy to change the way display modes work or add new ones. All you have to do is add a new class.
This is known as loose coupling.