S2(K(277))+
Proving the existence of a nonlift.
- The existence of a nonlift in S2(K(277))+
was already previously proven here as a quotient of a weight 4 paramodular form and a weight 2 paramodular form.
(The proof was part of the
this project
)
-
A nonlift Borcherds product Borch(ψ) in S2(K(277))+ can
be proven by constructing (the same) ψ explicitly in the following ways.
- Define ψ here
as a weight 12 cusp form divided by Δ
- Define ψ here as a sum Σj cj (φj|V2)/φj
- Define ψ here as (-φ|V2)/φ + c Θ/φ,
where Θ is an inflation of φ
-
Another nonlift Borcherds product Borch(ψ2) in S2(K(277))+ can
be proven by constructing (the same) ψ2 explicitly in the following ways.
- Define ψ2 here
as a weight 12 cusp form divided by Δ
- Define ψ2 here as Θ/φ,
where Θ is an inflation of φ
- The nonlift eigenform f in S2(K(277))+ has a formula as a linear combination of the first Borcherds product above
and Gritsenko lifts. See
here
for the formula.