The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A018898 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A018898

Theta series of 14-dimensional lattice of det 3^7 and minimal norm 2.
(history; published version)

#12 by Jon E. Schoenfield at Fri Sep 29 21:39:17 EDT 2023

STATUS

editing

approved

#11 by Jon E. Schoenfield at Fri Sep 29 21:39:15 EDT 2023

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#10 by Andrew Howroyd at Fri May 19 11:06:46 EDT 2023

STATUS

reviewed

approved

#9 by Joerg Arndt at Fri May 19 10:54:17 EDT 2023

STATUS

proposed

reviewed

#8 by Andy Huchala at Fri May 19 10:41:48 EDT 2023

STATUS

editing

proposed

#7 by Andy Huchala at Wed May 17 00:59:16 EDT 2023

COMMENTS

This is the same as A004048. - Andy Huchala, May 15 2023

Discussion

Fri May 19

10:41

Andy Huchala: I'm still confident this is the same as A004048, but I can't find a reference actually defining Gamma1(N)+ so I'll withdraw my comment.

#6 by Andy Huchala at Mon May 15 21:33:48 EDT 2023

COMMENTS

This is the same as A004048. - Andy Huchala, May 15 2023

STATUS

approved

editing

Discussion

Mon May 15

22:12

Andy Huchala: Per the reference Gross 1996 p. 276, this theta series is a weight 7 modular form on Gamma1(3)+. In "Normalizer of Gamma1(m)" by Lang, it is established that Normalizer(Gamma1(3))=Gamma0(3)+,  and in Zemel's "Normalizers of Congruence Groups in SL2(R)
and Automorphisms of Lattices" it's mentioned that Normalizer(Gamma0(3)) = Gamma0(3). I'm still looking for a reference to show that Gamma1(m)+ does in fact denote the normalizer of Gamma1(m) but I believe that's the intended meaning (Wikipedia mentions this for Gamma0(m)+).

All this to say... once I've found a reference (or if anyone can confirm this notation that Gamma1(N)+ means Normalizer(Gamma1(N)) both the theta series from this sequence and A004048 live in M_7(Gamma0(3)), which is 3-dimensional according to magma, so if they agree up to 3 terms they agree at every term.

#5 by Russ Cox at Fri Mar 30 16:46:30 EDT 2012

AUTHOR

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

Discussion

Fri Mar 30

16:46

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

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

KEYWORD

nonn,more,new

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

#3 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Theta series of 14-dim. dimensional lattice of det 3^7 and minimal norm 2.

KEYWORD

nonn,more,new

EXTENSIONS

Possibly the same as A004048?