I'm having hard time deciding which name to choose for my method. I think they both are pretty much self-explanatory, but the latter is faster to type, so, my current preference is supportedModes(). What do you think?
To me, getSupportedModes implies simple retrieval, whereas if there is some actual logic involved to work them out, something like determineSupportedModes or calculateSupportedModes may be better. The name should describe what the function does. Brevity is not a major consideration with modern IDEs with some form of autocomplete.
Different languages also have their own conventions. For example, a function called calculateSupportedModes in Java would normally be called CalculateSupportedModes in C# or VB.