The index of ${\mathbb{T}}^{\text{an}}$ in $\mathbb{T}$

For a prime level $N$, we compute the index of the anemic Hecke algebra of weight 2 level ${\mathrm{\Gamma }}_0(N)$ forms inside the full Hecke algebra. We prove that the index is fully described by the presence of weight 1 Katz forms of the same level.