Still can't figure out how to count spin

I still can't figure out how to count spin states, so I posted this question on stackexchange.com:

I can't figure out how many different spin states I can create with a four-electron system. I think I can create a spin-zero state, three spin-one states, and five spin-two states. That gives me nine possible states altogether. My problem is that I can specify a maximum of eight (complex) numbers to completely describe the spin states of the four electrons. But the nine spin-states I can seemingly create correspond to the spherical harmonic functions and I know for sure that they are linearly independent. It seems very wrong. This discrepancy in the counting doesn't appear until you get to four electrons. It gets worse as you add more electrons. Does anyone else have a problem with this?