  Let $\alpha\in(0,1)$ be irrational and $[0;a_1,a_2,\cdots]$ be the continued
fraction expansion of $\alpha$. Let $H_{\alpha,V}$ be the Sturm Hamiltonian
with frequency $\alpha$ and coupling $V$, $\Sigma_{\alpha,V}$ be the spectrum
of $H_{\alpha,V}$. The fractal dimensions of the spectrum have been determined
by Fan, Liu and Wen (Erg. Th. Dyn. Sys.,2011) when $\{a_n\}_{n\ge1}$ is
bounded. The present paper will treat the most difficult case, i.e,
$\{a_n\}_{n\ge1}$ is unbounded. We prove that for $V\ge24$, $$ \dim_H\
\Sigma_{\alpha,V}=s_*(V)\ \ \ \text{and}\ \ \ \bar{\dim}_B\
\Sigma_{\alpha,V}=s^*(V), $$ where $s_*(V)$ and $s^*(V)$ are lower and upper
pre-dimensions respectively. By this result, we determine the fractal
dimensions of the spectrums for all Sturm Hamiltonians.
  We also show the following results: $s_*(V)$ and $s^*(V)$ are Lipschitz
continuous on any bounded interval of $[24,\infty)$; the limits $s_*(V)\ln V$
and $s^*(V)\ln V$ exist as $V$ tend to infinity, and the limits are constants
only depending on $\alpha$; $s^\ast(V)=1$ if and only if
$\limsup_{n\to\infty}(a_1\cdots a_n)^{1/n}=\infty,$ which can be compared with
the fact: $s_\ast(V)=1$ if and only if $\liminf_{n\to\infty}(a_1\cdots
a_n)^{1/n}=\infty$(Liu and Wen, Potential anal. 2004).
