Extend supersingular trace formulas to the primes 2 and 3

Determine whether the supersingular trace formula and Brandt-module dot-product formula for the partition function can be extended to the primes 2 and 3 by using the normalization of the Deligne–Rapoport model of X_0(6) or an Igusa/Drinfeld–Cerednik uniformization.

Background

The paper proves supersingular trace and Brandt-module formulas for partition numbers modulo primes $\ell\geq 5$, relying on the geometry of the Deligne–Rapoport model of $X_0(6)$ away from the level primes. The primes 2 and 3 are excluded because they divide the level 6, causing additional singularities in the integral model and preventing the regularity argument used in the proof from applying directly.

The authors suggest two possible geometric tools for overcoming this obstruction: passing to the normalization of the Deligne–Rapoport model or using an Igusa/Drinfeld–Cerednik uniformization. Whether either approach yields the desired extension remains unresolved.