  We consider $\mathcal{N}=2$ supersymmetric $\text{SU}(2)$ gauge theory with
$N_f=4$ massive hypermultiplets. The duality group of this theory contains
transformations acting on the UV-coupling $\tau_{\text{UV}}$ as well as on the
running coupling $\tau$. We establish that subgroups of the duality group act
separately on $\tau_{\text{UV}}$ and $\tau$, while a larger group acts
simultaneously on $\tau_{\text{UV}}$ and $\tau$. For special choices of the
masses, we find that the duality groups can be identified with congruence
subgroups of $\text{SL}(2,\mathbb Z)$. We demonstrate that in such cases, the
order parameters are instances of bimodular forms with arguments $\tau$ and
$\tau_{\text{UV}}$. Since the UV duality group of the theory contains the
triality group of outer automorphisms of the flavour symmetry $\text{SO}(8)$,
the duality action gives rise to an orbit of mass configurations. Consequently,
the corresponding order parameters combine to vector-valued bimodular forms
with $\text{SL}(2,\mathbb Z)$ acting simultaneously on the two couplings.
