Characteristic Masses of Lattices
By Gaëtan Chenevier
This website is a companion to the paper
Characteristic Masses of Niemeier Lattices
by the author.
Documented source code of our
PARI/GP implementation of the algorithms of this paper:
masses_calc.gp
(tutorial).
1. Dimension of spaces of level 1 orthogonal automorphic forms
Nonzero dimensions for: O7, O8,
O9, O15, O16,
O17, O23, O24,
O25.
Format
Masses: O7, O8,
O9, O15, O16,
O17, O23, O24,
O25.
Format
2. Characteristic masses of even lattices of determinant 1 or 2
Dimension 7 (Gram):
E7.
Dimension 8 (Gram):
E8.
Dimension 9 (Gram):
A1_E8.
Dimension 15 (Gram):
E7_E8,
A1_D14.
Dimension 16 (Gram):
2E8,
D16.
Dimension 17 (Gram):
A1_2E8,
A1_D16,
A17,
D10_E7.
Dimension 23 (Gram):
A1_D22,
A1_D14_E8,
D16_E7,
E7_2E8,
A22,
A1_D10_D12,
A15_E7,
A17_D6,
A1_D8_2E7,
D10_D6_E7,
A13_D9,
A1_A15_D7,
A1_D6_2D8,
A10_A12,
A9_D7_E6,
A1_A11_D5_E6,
A11_A5_D7,
A5_3E6,
A7_A9_D6,
A1_2A9_D4,
A1_D4_3D6,
A6_2A8,
A5_A7_2D5,
A1_A3_2A7_D5,
A4_3A6,
A3_3A5_D4,
3A1_4A5,
3A1_5D4,
A2_5A4,
A1_7A3,
11A2,
23A1.
Dimension 24 (Niemeier lattices, Gram):
D24,
D16_E8,
3E8,
A24,
2D12,
A17_E7,
D10_2E7,
A15_D9,
3D8,
2A12,
A11_D7_E6,
4E6,
2A9_D6,
4D6,
3A8,
2A7_2D5,
4A6,
4A5_D4,
6D4,
6A4,
8A3,
12A2,
24A1,
Leech.
Dimension 25 (Gram):
A1,
A2,
9A1,
12A1_A2,
25A1,
9A1_4A2,
15A1_A3,
9A2,
6A1_5A2_A3,
A1_12A2,
3A1_4A2_3A3,
9A1_4A3,
5A1_6A2_A4,
21A1_D4,
A2_6A3,
2A1_3A2_3A3_A4,
9A2_D4,
A1_8A3,
A1_4A3_2A4,
3A1_2A2_A3_3A4,
3A1_5A3_D4,
4A2_3A3_A5,
6A1_4A3_A5,
3A2_3A4_D4,
A1_A2_2A3_2A4_A5,
A1_6A4,
9A1_4D4,
3A3_A5_2D4,
A1_A3_2A4_2A5,
3A1_2A3_2A5_D4,
4A2_3A5,
A1_6A3_D5,
A1_A2_2A3_2A4_A6,
A2_4A5,
A2_4A4_D5,
3A4_A6_D4,
2A2_A3_2A5_A6,
A1_4A5_D4,
A1_A3_2A5_D4_D5,
4A1_3A5_D5,
A1_6D4,
2A1_A4_A5_2A6,
A3_2A4_A5_A7,
2A1_2A3_A5_A7_D4,
A2_A4_2A6_D5,
3A6_D4,
A1_A4_A5_A6_A7,
A1_4A6,
A3_A5_3D5,
3A1_4D4_D6,
A3_3A5_D6,
A1_2A3_A7_2D5,
A1_2A7_2D4,
3A5_A8,
A2_A3_A5_A6_A8,
A2_3A7,
A4_A6_A8_D5,
A1_2A7_2D5,
3A5_D4_E6,
A5_A7_D5_D6,
A1_A3_2A7_D6,
A1_2A7_A8,
A1_A5_A9_D4_D5,
2A4_A7_A9,
3A6_E6,
A2_A5_A8_A9,
A1_3A8,
3A1_D4_3D6,
A1_A7_2D5_E6,
A5_A7_D5_D7,
A1_A3_2A7_D7,
2A1_A7_A9_D6,
A1_A10_A6_A7,
A2_2A8_E6,
A10_A8_D5,
A1_2A9_D6,
A11_A3_A5_D6,
A11_A5_A8,
A1_4D6,
A3_A9_D6_E6,
A5_D7_2E6,
A1_D4_2D6_D8,
A9_2D7,
A7_A9_D8,
A1_A11_D5_D7,
2A11_A2,
A12_A6_E6,
A1_A11_D7_E6,
A13_D5_D6,
A1_4E6,
A1_A10_A13,
A1_2A12,
3D6_E7,
2A9_E7,
A9_D9_E6,
A11_A5_D9,
A14_A2_A9,
A11_E6_E7,
A1_3D8,
2A1_2D8_E7,
A1_D10_D6_D8,
A1_A15_D8,
A1_A15_D9,
A15_A3_E7,
A17_A8,
D4_3E7,
A13_D11,
A18_E6,
A1_A17_E7,
A1_D10_2E7,
D12_D6_E7,
A1_2D12,
D10_E7_E8,
A1_D10_D14,
A17_E8,
A2_A23,
A1_A24,
A1_D16_E8,
A1_3E8,
D18_E7,
A1_D24.
Format