S2(K(523))+
Proving the existence of a nonlift.
-
A nonlift Borcherds product Borch(ψ) in S2(K(523))+
can
be proven by constructing 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
- Once the existence of a nonlift in S2(K(523))+ is proven using the above arguments,
the previously conjectured formula for the nonlift eigenform f in S2(K(523))+
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
)
- The above nonlift eigenform f also has a formula as a linear combination of the above Borcherds product
and Gritsenko lifts. See
here
for the formula.