Makdisi for X(N)
Need line bundle L:
Pick L whose sections are modular forms of weight 2.
Need points P1, · · · , Pn to evaluate forms at:
Fix (E, α), take the
(E, α ◦ γ)
for γ ∈ SL2(Z/NZ)/ ± 1.
Still need to “evaluate” a basis of the space of forms of
weight 2 at the Pi ...
Nicolas Mascot p-adic computation of Galois representations