The known extremal strongly modular lattices of level 2,3,5,6,7,11,14,15,23

This table was originally created by Michael Juergens during his dissertation project as: Extremal lattices It is maintained and updated here by Gabriele Nebe.

Keywords: modular lattices, tables, minimal norm, quadratic forms

Part of the Catalogue of Lattices which is a joint project of Gabriele Nebe, RWTH Aachen university (nebe@math.rwth-aachen.de) and Neil J. A. Sloane, (njasloane@gmail.com).

A strongly N-modular lattice is an even lattice of even level N which is similar to all its partial dual lattices. Extremal strongly modular lattices are those lattices of square free level N with divisor sum dividing 24 for which the minimum is as high as the theory of modular forms allows it to be, for a precise definition see Quebbemann, H.-G. Atkin-Lehner eigenforms and strongly modular lattices. Enseign. Math. (2) 43 (1997).

	2	3	5	6a	6b	7	11	14	15	23
2	-	1	-	-	-	1	1	-	-	1
4	1	1	1	1	1	1	1	1	1	1
6	-	1	-	-	-	1	1	-	-	-
8	1	2	1	1		1	1	1	2	-
10	-	3	-	-	-	4	2	-	-	-
12	3	1	4	6	4	0	0	1	3 (5)	-
14	-	1	-	-	-	1	?	-	-	-
16	1	6	1	8		≥ 18	-	?	≥ 1	-
18	-	37	-	-	-	0	?	-	-	-
20	3	≥ 100	≥ 72	?	≥ 13	≥ 1	-	?	?	-
22	-	≥ 1000	-	-	-	?	?	-	-	-
24	≥ 8	≥ 1	≥ 1	≥ 2		0	-	?	?	-
26	-	≥ 6	-	-	-	?	-	-	-	-
28	≥ 24	≥ 9	≥ 1	?	?	?	-	?	?	-
30	-	≥ 2	-	-	-	-	-	-	-	-
32	≥ 7	≥ 33	?	?		?	-	-	-	-
34	-	≥ 100	-	-	-	?	-	-	-	-
36	≥ 3	?	?	?	?	-	-	-	-	-
38	-	?	-	-	-	?	-	-	-	-
40	≥ 6	≥ 1	?	?		?	-	-	-	-
42	-	?	-	-	-	-	-	-	-	-
44	≥ 1	?	?	?	?	-	-	-	-	-
46	-	?	-	-	-	?	-	-	-	-
48	≥ 6	?	?	?		-	-	-	-	-