On Some Open Cases of a Conjecture of Conrad, Edixhoven and Stein

Let $p\ge 5$ be a prime. In 2003 Conrad, Edixhoven, and Stein conjectured that the rational torsion subgroup of the modular Jacobian $J_1(p)$ coincides with the rational cuspidal divisor class group. Using explicit computations in Magma, the open case $p=29$ has been proven by Derickx, Kamienny, Stein, and Stoll in 2023. We extend these results to primes $p=97,101,109,$ and $113$. In addition, we provide a list of the groups $J_1(p)(\mathbb{Q}{)}_{\text{tors}}$ for every prime up to $p\le 113$. However, our method is general and can be applied to larger primes.