A Borcherds Product in S2(K(277))+

(Filename: BP-2-277-1-0-8-hs.html)

DEFINITION OF ψ AND BORCH(ψ)
The weakly holomorphic Jacobi form ψ of weight 0 and index 277, is defined as
    ψ = Σj=13 cj (φj|V2)/φj
where the coefficients cj and theta blocks φj are given as follows. Note each φj ∈ J2,277cusp with ν(φj) = 1.
cjφj
1
TB(2;1,2,2,3,4,6,8,8,10,16)
-1
TB(2;2,2,3,4,4,6,7,8,10,16)
-1
TB(2;1,2,3,3,5,6,8,9,10,15)
Note that BORCH(ψ) has leading Jacobi coefficient the theta block φ ∈ J2,277cusp, with ν(φ) = 1,
     φ = TB(2;2,3,3,4,5,6,7,9,10,15)
= 21324151617191101151
= η(τ)4(θ(τ,2z)/η(τ))(θ(τ,3z)/η(τ))2(θ(τ,4z)/η(τ))(θ(τ,5z)/η(τ))(θ(τ,6z)/η(τ))(θ(τ,7z)/η(τ))(θ(τ,9z)/η(τ))(θ(τ,10z)/η(τ))(θ(τ,15z)/η(τ))
and so BORCH(ψ) begins with Jacobi coefficient #1.

PROPERTIES OF ψ AND BORCH(ψ)
See this page for properties of ψ and BORCH(ψ), such as Humbert divisors of BORCH(ψ) and some Fourier coefficients of BORCH(ψ).