  We study the canonical Hodge filtration on the sheaf $\mathscr{O}_X(*D)$ of
meromorphic functions along a divisor. For a germ of an analytic function $f$
whose Bernstein-Sato's polynomial's roots are contained in $(-2,0)$, we: give a
simple algebraic formula for the zeroeth piece of the Hodge filtration; bound
the first step of the Hodge filtration containing $f^{-1}$. If we additionally
require $f$ to be Euler homogeneous and parametrically prime, then we extend
our algebraic formula to compute every piece of the canonical Hodge filtration,
proving in turn that the Hodge filtration is contained in the induced order
filtration. Finally, we compute the Hodge filtration in many examples and
identify several large classes of divisors realizing our theorems.
