p=5 j=1: #normal subgroups of index<=p^j = 7; 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=5 j=2: #normal subgroups of index<=p^j = 13; 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
