S2(K(461))+
Proving the existence of a nonlift.
-
There are no nonlift Borcherds product in S2(K(461))+
- A [nonlift] Borcherds product Borch(ψ) in S2(K(922))−
can be proven by constructing ψ explicitly
here
as (φ|V2)/φ + (a weight 12 cusp form divided by Δ)
- Note that Borch(ψ)|AL2 − Borch(ψ)
∈ S2(K(922))− +.
We trace down Borch(ψ)|AL2 − Borch(ψ) to S2(K(461))+
and show that the result is not in the subspace of Gritsenko lifts, thus
proving that there is a nonlift in S2(K(461))+.
- Once the existence of a nonlift in S2(K(461))+ is proven using the above arguments,
the previously conjectured formula for the nonlift eigenform f in S2(K(461))+
as a quotient f = Q/L of a weight 4 paramodular form with a weight 2 paramodular form becomes a theorem.
See
here for the formula f = Q/L.
(The formula was part of
this project
)