of this flag with respect to the Hodge filtration on $D_{\rm cris}(\rho_{x,v})$, see §\[weyl\] (where we rather use another equivalent definition of $w_{x,v}$ in terms of triangulations). Following [@BelChe §2.4.3] we say that $x$ is [*noncritical*]{} if, for each $v$, the permutation $w_{x,v}$ is trivial. The invariant $(w_{x,v})_{v\in S_p}$ can thus be seen as “measuring” the criticality of $x$.

In the statement of our main theorem, we need to assume a certain number of Working Hypotheses (basically the combined hypotheses of all the papers we use). We denote by ${\overline{\rho}}_x$ the mod $p$ semi-simplification of $\rho_x$. These Working Hypotheses are:

1.  The field $F$ is unramified over $F^+$ and $G$ is quasi-split at all finite places of $F^+$;

2.  the tame level of $x$ is hyperspecial at all finite places of $F^+$ inert in $F$;

3.  ${\overline{\rho}}_x({\rm Gal}(\overline F/F(\zeta_p))$ is adequate ([@Thorne]) and $\zeta_p\notin \overline F^{\ker({\rm ad}{\overline{\rho}}_x)}$;

4.  the eigenvalues of $\varphi$ on $D_{\rm cris}(\rho_{x,v})$ are sufficiently generic for any $v\in S_p$ (Definition \[veryreg\]).

Our main theorem is:

\[mainintro\] Let $p>2$ and assume that the group $G$ and the tame level satisfy (i) and (ii). Let $x$ be an overconvergent form of classical weight such that $\rho_x$ is crystalline and 