Conjecture on rational torsion orders for GL2-type abelian varieties

Let $A/\mathbb Q$ be a $g$-dimensional abelian variety of $\operatorname{GL}_2$-type. Its rational torsion subgroup is $\operatorname{Tors}(A)(\mathbb Q)$.

Torsion-order conjecture. The possible orders $|\operatorname{Tors}(A)(\mathbb Q)|$ are precisely the integers listed below:

• If $g=2$, they are $1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,24,28,44,56$.
• If $g=3$, they are $1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,20,22,23,28,29,31,32,40,44,46,58,80,92$.

The lists are based on computational evidence from predicted torsion orders, and the authors do not know whether they are exhaustive; the conjecture concerns dimensions $2$ and $3$.