  We study twisted circle compactification of 6d $(2,0)$ SCFTs to 5d
$\mathcal{N} = 2$ supersymmetric gauge theories with non-simply-laced gauge
groups. We provide two complementary approaches towards the BPS partition
functions, reflecting the 5d and 6d point of view respectively. The first is
based on the blowup equations for the instanton partition function, from which
in particular we determine explicitly the one-instanton contribution for all
simple Lie groups. The second is based on the modular bootstrap program, and we
propose a novel modular ansatz for the twisted elliptic genera that transform
under the congruence subgroups $\Gamma_0(N)$ of $\text{SL}(2,\mathbb{Z})$. We
conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the
genus one fibered Calabi-Yau threefolds, upon which one can determine the
twisted elliptic genera recursively. We use our results to obtain the 6d Cardy
formulas and find universal behaviour for all simple Lie groups. In addition,
the Cardy formulas remain invariant under the twist once the normalization of
the compact circle is taken into account.
