Algebraic modular forms
Definition
An algebraic modular form of weight k for X(N) over R is a
rule f assigning a value to pairs (E/R, α), such that
f (E0
, α) = uk
f (E, α)
for all u ∈ R×
.
Examples
E 7→ A is a modular form of weight 4.
E 7→ ∆ := −64A3
− 432B2
is a modular form of weight 12.
by (x, y) 7→ (u2
x, u3
y), A0
= u4
A, B0
= u6
B, ω0
= u−1
ω.
Nicolas Mascot p-adic computation of Galois representations