Step 4: Admissible points
We want to find functions on Ef whose pull-back to X1(N) are modular
units. We define
S =

p ∈ Ef : ϕ−1
(p) ⊂ {cusps}
	
⊂ {p1, . . . , ps}.
Then for any function h on E supported in S, ϕ∗
(h) is a modular unit.
1. Compute the modular degree deg(ϕ) using mfpetersson and
Z
X1(N)
ωf ∧ ωf = deg(ϕ) ·
Z
Ef
ωEf
∧ ωEf
.
2. For each cusp c, compute the ramification index eϕ(c) using
mfslashexpansion.
3. For each point p ∈ ϕ({cusps}), check whether
X
c cusp
ϕ(c)=p
eϕ(c) = deg(ϕ).
If true, put p in S.
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