You should try by hand to show that in this same single-particle space, that for \( N=3 \) there are 3 states with \( M=1/2 \) and for \( N= 4 \) there are also only 3 states with \( M=0 \).

To test your code, confirm the above.

Also, for the \( sd \)-space given above, for \( N=2 \) there are 14 states with \( M=0 \), for \( N=3 \) there are 37 states with \( M=1/2 \), for \( N=4 \) there are 81 states with \( M=0 \).