k=1 |H_k| = 2 = 2^1
k=2 |H_k| = 8 = 2^3
k=3 |H_k| = 32 = 2^5
k=4 |H_k| = 256 = 2^8
k=5 |H_k| = 2048 = 2^11
k=6 |H_k| = 16384 = 2^14
k=7 |H_k| = 131072 = 2^17
first m >= 2 with |H_{m+1}| = 8|H_m| : m = 3
k=3  H_k == Q_k : True   (|Q_k| = 32)
k=4  H_k == Q_k : True   (|Q_k| = 256)
k=5  H_k == Q_k : True   (|Q_k| = 2048)
k=6  H_k == Q_k : True   (|Q_k| = 16384)
k=7  H_k == Q_k : True   (|Q_k| = 131072)
index [PGL_2(Z_2) : H] = 6*8^(m-1)/|H_m| = 12
|H_k| = |H_m| 8^(k-m) for m <= k <= KMAX: True
