  Let $\Gamma_{w}$ be a non-cofinite Hecke triangle group with cusp width $w>2$
and let $\varrho\colon\Gamma_w\to U(V)$ be a finite-dimensional unitary
representation of $\Gamma_w$. In this note we announce a new fractal upper
bound for the Selberg zeta function of $\Gamma_{w}$ twisted by $\varrho$. In
strips parallel to the imaginary axis and bounded away from the real axis, the
Selberg zeta function is bounded by $\exp\left( C_{\varepsilon} \vert
s\vert^{\delta + \varepsilon} \right)$, where $\delta = \delta_{w}$ denotes the
Hausdorff dimension of the limit set of $\Gamma_{w}$. This bound implies
fractal Weyl bounds on the resonances of the Laplacian for all geometrically
finite surfaces $X=\widetilde{\Gamma}\backslash\mathbb{H}$ where
$\widetilde{\Gamma}$ is a finite index, torsion-free subgroup of $\Gamma_w$.
