Let $W = \{ p(B) : p \text{ is a polynomial with real coefficients}\}$, where $$B= \begin{pmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 0 & 0 \end{pmatrix}$$
Which of the following possibilities presents the tightest bounds on the dimension $d$ of the vector space $W$?
- $4 ≤ d ≤ 6$
- $6 ≤ d ≤ 9$
- $3 ≤ d ≤ 8$
- $3 ≤ d ≤ 4$