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A362875 Theta series of 15-dimensional lattice Kappa_15. 7
1, 0, 1746, 21456, 147150, 607536, 2036334, 5410800, 13282866, 27563184, 56679732, 102040272, 184563384, 302221728, 504866340, 763016400, 1202127174, 1728479808, 2575653198, 3561176016, 5127122304, 6797385072, 9531403128, 12329627616, 16701654486, 21199654080 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Theta series is an element of the space of modular forms on Gamma_1(48) with Kronecker character 12 in modulus 48, weight 15/2, and dimension 58 over the integers.
REFERENCES
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Chap. 6.
LINKS
G. Nebe and N. J. A. Sloane, Home page for this lattice.
EXAMPLE
G.f. = 1 + 1746*q^4 + 21456*q^6 + 147150*q^8 + ...
PROG
(Magma)
prec := 70;
S := SymmetricMatrix([4, 2, 4, 0, -2, 4, 0, -2, 0, 4, 0, 0, -2, 0, 4, -2, -2, 0, 0, 0, 4, -2, -1, 1, 0, 0, 0, 4, -2, -1, 0, -1, 1, 2, 2, 4, -2, -2, 0, 1, 1, 2, 2, 2, 4, -2, 0, -2, 0, 1, 1, 0, 0, 0, 4, 1, 1, 0, 0, 0, -2, 0, -1, -1, -2, 4, -2, -1, 0, 0, 0, 1, 1, 1, 1, 1, -2, 4, 0, -1, 1, 1, 0, -1, 1, 0, 0, -1, 1, -1, 4, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1, 1, -1, 1, 4, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 0, 0, -1, 4]);
ls := [1, 0, 1746, 21456, 147150, 607536, 2036334, 5410800, 13282866, 27563184, 56679732, 102040272, 184563384, 302221728, 504866340, 763016400, 1202127174, 1728479808, 2575653198, 3561176016, 5127122304, 6797385072, 9531403128, 12329627616, 16701654486, 21199654080, 28230179220, 34817427648, 45678519396, 55628679312, 71267532432, 85814825328, 108809427618, 128313065808, 161435864196, 188866349856, 233000967122, 271038881664, 332652360024, 380052936000, 464058384948, 528207272064, 634933480440, 719891109360, 862226645076, 963402396336, 1151630548200, 1283383148256, 1511712192624, 1682610190272, 1980149372586, 2173335020640, 2553938906832, 2802302452080, 3252053197962, 3565107859680, 4134281599332, 4478370612624];
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[ls[i] * B[i] : i in [1..58]]);
CROSSREFS
Sequence in context: A260014 A190829 A038010 * A324710 A201801 A172833
KEYWORD
nonn
AUTHOR
Andy Huchala, May 07 2023
STATUS
approved

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Last modified December 8 23:37 EST 2023. Contains 367681 sequences. (Running on oeis4.)