Unprecedented size of the $q$-structure in AdS$_3$ and $\mathcal{N}=2$ supergravity

We show that the $q$-structure in AdS$_3$ and $\mathcal{N}=2$ supergravity can be obtained by the non-canonical solution of the AdS$_3$ and $\mathcal{N}=2$ supergravity equations. This result is in striking contrast to previous results that the $q$-structure is well-behaved in both AdS$_2$ and $\mathcal{N}=2$ supergravity.