I Why spin matrixes number of rows depends of spinn magnitude?

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Why spin-matrixes and spinors have more rows for particles with greater spin (https://en.wikipedia.org/wiki/Spin_(physics)#Higher_spins)? As I understand every row is for 1 spin orientation, but why does number of possible orientations depend of magnitude of spin?
 
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olgerm said:
Why spin-matrixes and spinors have more rows for particles with greater spin (https://en.wikipedia.org/wiki/Spin_(physics)#Higher_spins)? As I understand every row is for 1 spin orientation, but why does number of possible orientations depend of magnitude of spin?
These aren't defined by spin orientations, these are the defined by the number of spin eigenstates.
 
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