p=3 j=1: #normal subgroups of index<=p^j = 5; I_j: top p^1, I_j cap B = B_1 (ideal: True); predicted S(j, b_max) with b_max=1: True; log_p|W:I_j| = 2
p=3 j=2: #normal subgroups of index<=p^j = 9; I_j: top p^2, I_j cap B = B_1 (ideal: True); predicted S(j, b_max) with b_max=1: True; log_p|W:I_j| = 3
p=3 j=3: #normal subgroups of index<=p^j = 16; I_j: top p^3, I_j cap B = B_2 (ideal: True); predicted S(j, b_max) with b_max=2: True; log_p|W:I_j| = 5
