Emerton's dimension conjecture for the full Hecke algebra at p = 2 and odd level

Theorem 1.1: for every odd $N$, every irreducible component of $\mathrm{Spec}\,\mathbb T_2(N)$ has Krull dimension exactly $4$. The upper bound comes from a cuspidal point of weight at least 3 on each component, a tangent bound of 3 from Newton-Thorne Selmer vanishing, and one arithmetic dimension. Only the case $p=2$ is treated; the paper does not claim the conjecture for odd $p$.

Theorem 1.1: for every odd $N$, every irreducible component of $\mathrm{Spec}\,\mathbb T_2(N)$ has Krull dimension exactly $4$. The upper bound comes from a cuspidal point of weight at least 3 on each component, a tangent bound of 3 from Newton-Thorne Selmer vanishing, and one arithmetic dimension. Only the case $p=2$ is treated; the paper does not claim the conjecture for odd $p$.