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A033699

Theta series of lattice A_2 tensor E_7 (dimension 14, determinant 8748, minimal norm 4).
(history; published version)

#15 by OEIS Server at Sat May 13 13:27:09 EDT 2023

LINKS

Andy Huchala, <a href="/A033699/b033699_1.txt">Table of n, a(n) for n = 0..20000</a>

#14 by N. J. A. Sloane at Sat May 13 13:27:09 EDT 2023

STATUS

proposed

approved

Discussion

Sat May 13

13:27

OEIS Server: Installed first b-file as b033699.txt.

#13 by Michel Marcus at Sat May 13 11:31:27 EDT 2023

STATUS

editing

proposed

#12 by Michel Marcus at Sat May 13 11:31:23 EDT 2023

EXTENSIONS

Edited by N. J. A. Sloane Aug 31 2009 at the suggestion of _R. J. Mathar._

More terms from Andy Huchala, May 13 2023.

STATUS

proposed

editing

#11 by Andy Huchala at Sat May 13 11:27:25 EDT 2023

STATUS

editing

proposed

#10 by Andy Huchala at Sat May 13 11:26:45 EDT 2023

LINKS

Andy Huchala, <a href="/A033699/b033699_1.txt">Table of n, a(n) for n = 0..20000</a>

EXTENSIONS

More terms from Andy Huchala, May 13 2023.

#9 by Andy Huchala at Sat May 13 03:17:11 EDT 2023

DATA

1, 0, 378, 4032, 24948, 84672, 272706, 689472, 1471554, 3003840, 6041952, 9640512, 17409420, 28304640, 42284052, 64338624, 101413620, 131362560, 198388554, 275679936, 359236080, 484706880, 685716192, 805569408, 1113880362, 1430763264, 1734830244, 2189464704

COMMENTS

Theta series is an element of the space of modular forms on Gamma_1(6) with Kronecker character -3 in modulus 6, weight 7, and dimension 8 over the integers. - Andy Huchala, May 13 2023

EXAMPLE

G.f. = 1 + 378*q^4 + 4032*q^6 + ...

PROG

(Magma)

prec := 20;

ls := [[4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -2, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 1, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, -2, -2, 4, 1, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 1, 4, -2, -2, 1, 0, 0, -2, 1], [0, 0, 0, 0, 1, -2, -2, 4, 1, -2, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0, -2, 1, 4, -2, -2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -2, -2, 4, 1, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 4, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 4, 0, 0], [0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 4, -2], [0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -2, 4]];

S := Matrix(ls);

L := LatticeWithGram(S);

M := ThetaSeriesModularFormSpace(L);

B := Basis(M, prec);

coeffs := [1, 0, 378, 4032, 24948, 84672, 272706, 689472];

Coefficients(&+[coeffs[i]*B[i] :i in [1..8]]); // Andy Huchala, May 13 2023

KEYWORD

nonn,more

nonn

STATUS

approved

editing

#8 by Russ Cox at Fri Mar 30 16:47:25 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com)_.

EXTENSIONS

Edited by _N. J. A. Sloane (njas(AT)research.att.com) _ Aug 31 2009 at the suggestion of R. J. Mathar.

Discussion

Fri Mar 30

16:47

OEIS Server: https://oeis.org/edit/global/110

#7 by N. J. A. Sloane at Wed Oct 20 03:00:00 EDT 2010

LINKS

G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/P14.3.html">Home page for this lattice</a>

KEYWORD

nonn,more,new

#6 by N. J. A. Sloane at Sun Sep 12 03:00:00 EDT 2010

LINKS

G. Nebe and N. J. A. Sloane, <a href="http://www.researchmath.attrwth-aachen.comde/~njasGabriele.Nebe/latticesLATTICES/P14.3.html">Home page for this lattice</a>

KEYWORD

nonn,more,new