$L(t) = \det(1 - t\operatorname{Frob} \mid H^1) = 1 - 3t + 14t^2 - 93t^3 + 961t^4.$

$\operatorname{Frob}|_{H^1_{\mathrm{dR}}(A/\mathbf{Q}_p)} \equiv \begin{pmatrix} 31 \cdot 482 & 31 \cdot 284 & 16241 & 3075 \\ 31 \cdot 386 & 31 \cdot 886 & 2644 & 12126 \\ 31 \cdot 284 & 31 \cdot 659 & 6336 & 9750 \\ 31 \cdot 194 & 31 \cdot 876 & 27408 & 10841 \end{pmatrix} \pmod{31^3},$

From this we deduce $\operatorname{Frob}|_{H^2_{\mathrm{dR}}(A/\mathbf{Q}_p)}$ and

$\det(1 - t\,31^{-1}\operatorname{Frob} \mid H^2_{\mathrm{dR}}(A/\mathbf{Q}_p)) = (t-1)^2(31t^4 + 48t^3 + 43t^2 + 48t + 31)/31$

Thus, $\rho\bigl(A_{\mathbf{F}_p^{\mathrm{al}}}\bigr) = 2$.

Since the basis of $H^1$ respects the Hodge filtration, the induced basis in $H^2$ will also respect it.