

A056945


Jacobi form of weight 12 and index 1 associated to a (nonexistent) lattice vector of norm 2 for the Leech lattice.


1



1, 0, 0, 4, 6, 0, 0, 32736, 131076, 0, 0, 3669012, 9172952, 0, 0, 95691552, 188239518, 0, 0, 1142929524, 1959705000, 0, 0, 8506686816, 13293227112, 0, 0, 45763087664, 67073100864, 0, 0, 195387947712, 272567759508, 0, 0, 698077783656, 938807478318, 0, 0, 2176654050912
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OFFSET

0,4


COMMENTS

Let J(h)=E_8*E_{4,1}+(2h60)*phi_{12,1} be the Jacobi form of weight 12 and index 1 associated with a norm 2 vector of a Niemeier lattice of Coxeter number h. Let J(h)=sum_{n,r} c(4nr^2) q^n*z^r. So a(n)=c(4mr^2) for h=0.
Let N(h,n) be the number of vectors of norm 2n for the lattice, then we have N(h,n)=c(4n)+2*sum_{1<=r<=sqrt(4n)}c(4nr^2) if h is the Coxeter number of a Niemeier lattice. Note that N(0,n)=a(4n)2*sum a(4nr^2)=A008408(n), for the Leech lattice! Note also a(3)<0 and a(n) is nonnegative for n<=1000, except 3.


REFERENCES

Eichler and Zagier, The Theory of Jacobi Forms, Birkhauser, 1985.


LINKS

Table of n, a(n) for n=0..39.


FORMULA

E_8*E_{4, 1}60*phi_{12, 1}. The E's are EisensteinJacobi series and phi_{12, 1} is the unique normalized Jacobi cusp form of weight 12 and index 1.


CROSSREFS

Cf. A008408, A056946.
Sequence in context: A079207 A259825 A276449 * A324472 A070683 A195785
Adjacent sequences: A056942 A056943 A056944 * A056946 A056947 A056948


KEYWORD

sign


AUTHOR

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 16 2000


STATUS

approved



