Parameters: D = 184, A = 7, B = 190, X = 1518.
This page records the compact basis and Gram matrix for the lattice obtained from the primitive isotropic vector
w = (0,7,8,...,190;1518) in II_{185,1}.
Reference: A Lorentzian Construction in Dimension 88 and Infinitely Many Further Ranks.
We use the ambient basis [g, delta_1, ..., delta_184, h] of II_{185,1}, where g=(1/2,...,1/2,-1/2), delta_j=e_{j+1}-e_{j+2} for j=1,...,D, and h=e_{D+1}+e_{D+2}.
Download: conway-lattice-D184-basis.txt
b_1 = 1:1, 2:9821 b_2 = 2:1, 3:2, 4:-3 b_3 = 4:-1, 5:1 b_4 = 5:-1, 6:1 b_5 = 6:-1, 7:1 b_6 = 7:-1, 8:1 b_7 = 8:-1, 9:1 b_8 = 9:-1, 10:1 b_9 = 10:-1, 11:1 b_10 = 11:-1, 12:1 b_11 = 12:-1, 13:1 b_12 = 13:-1, 14:1 b_13 = 14:-1, 15:1 b_14 = 15:-1, 16:1 b_15 = 16:-1, 17:1 b_16 = 17:-1, 18:1 b_17 = 18:-1, 19:1 b_18 = 19:-1, 20:1 b_19 = 20:-1, 21:1 b_20 = 21:-1, 22:1 b_21 = 22:-1, 23:1 b_22 = 23:-1, 24:1 b_23 = 24:-1, 25:1 b_24 = 25:-1, 26:1 b_25 = 26:-1, 27:1 b_26 = 27:-1, 28:1 b_27 = 28:-1, 29:1 b_28 = 29:-1, 30:1 b_29 = 30:-1, 31:1 b_30 = 31:-1, 32:1 b_31 = 32:-1, 33:1 b_32 = 33:-1, 34:1 b_33 = 34:-1, 35:1 b_34 = 35:-1, 36:1 b_35 = 36:-1, 37:1 b_36 = 37:-1, 38:1 b_37 = 38:-1, 39:1 b_38 = 39:-1, 40:1 b_39 = 40:-1, 41:1 b_40 = 41:-1, 42:1 b_41 = 42:-1, 43:1 b_42 = 43:-1, 44:1 b_43 = 44:-1, 45:1 b_44 = 45:-1, 46:1 b_45 = 46:-1, 47:1 b_46 = 47:-1, 48:1 b_47 = 48:-1, 49:1 b_48 = 49:-1, 50:1 b_49 = 50:-1, 51:1 b_50 = 51:-1, 52:1 b_51 = 52:-1, 53:1 b_52 = 53:-1, 54:1 b_53 = 54:-1, 55:1 b_54 = 55:-1, 56:1 b_55 = 56:-1, 57:1 b_56 = 57:-1, 58:1 b_57 = 58:-1, 59:1 b_58 = 59:-1, 60:1 b_59 = 60:-1, 61:1 b_60 = 61:-1, 62:1 b_61 = 62:-1, 63:1 b_62 = 63:-1, 64:1 b_63 = 64:-1, 65:1 b_64 = 65:-1, 66:1 b_65 = 66:-1, 67:1 b_66 = 67:-1, 68:1 b_67 = 68:-1, 69:1 b_68 = 69:-1, 70:1 b_69 = 70:-1, 71:1 b_70 = 71:-1, 72:1 b_71 = 72:-1, 73:1 b_72 = 73:-1, 74:1 b_73 = 74:-1, 75:1 b_74 = 75:-1, 76:1 b_75 = 76:-1, 77:1 b_76 = 77:-1, 78:1 b_77 = 78:-1, 79:1 b_78 = 79:-1, 80:1 b_79 = 80:-1, 81:1 b_80 = 81:-1, 82:1 b_81 = 82:-1, 83:1 b_82 = 83:-1, 84:1 b_83 = 84:-1, 85:1 b_84 = 85:-1, 86:1 b_85 = 86:-1, 87:1 b_86 = 87:-1, 88:1 b_87 = 88:-1, 89:1 b_88 = 89:-1, 90:1 b_89 = 90:-1, 91:1 b_90 = 91:-1, 92:1 b_91 = 92:-1, 93:1 b_92 = 93:-1, 94:1 b_93 = 94:-1, 95:1 b_94 = 95:-1, 96:1 b_95 = 96:-1, 97:1 b_96 = 97:-1, 98:1 b_97 = 98:-1, 99:1 b_98 = 99:-1, 100:1 b_99 = 100:-1, 101:1 b_100 = 101:-1, 102:1 b_101 = 102:-1, 103:1 b_102 = 103:-1, 104:1 b_103 = 104:-1, 105:1 b_104 = 105:-1, 106:1 b_105 = 106:-1, 107:1 b_106 = 107:-1, 108:1 b_107 = 108:-1, 109:1 b_108 = 109:-1, 110:1 b_109 = 110:-1, 111:1 b_110 = 111:-1, 112:1 b_111 = 112:-1, 113:1 b_112 = 113:-1, 114:1 b_113 = 114:-1, 115:1 b_114 = 115:-1, 116:1 b_115 = 116:-1, 117:1 b_116 = 117:-1, 118:1 b_117 = 118:-1, 119:1 b_118 = 119:-1, 120:1 b_119 = 120:-1, 121:1 b_120 = 121:-1, 122:1 b_121 = 122:-1, 123:1 b_122 = 123:-1, 124:1 b_123 = 124:-1, 125:1 b_124 = 125:-1, 126:1 b_125 = 126:-1, 127:1 b_126 = 127:-1, 128:1 b_127 = 128:-1, 129:1 b_128 = 129:-1, 130:1 b_129 = 130:-1, 131:1 b_130 = 131:-1, 132:1 b_131 = 132:-1, 133:1 b_132 = 133:-1, 134:1 b_133 = 134:-1, 135:1 b_134 = 135:-1, 136:1 b_135 = 136:-1, 137:1 b_136 = 137:-1, 138:1 b_137 = 138:-1, 139:1 b_138 = 139:-1, 140:1 b_139 = 140:-1, 141:1 b_140 = 141:-1, 142:1 b_141 = 142:-1, 143:1 b_142 = 143:-1, 144:1 b_143 = 144:-1, 145:1 b_144 = 145:-1, 146:1 b_145 = 146:-1, 147:1 b_146 = 147:-1, 148:1 b_147 = 148:-1, 149:1 b_148 = 149:-1, 150:1 b_149 = 150:-1, 151:1 b_150 = 151:-1, 152:1 b_151 = 152:-1, 153:1 b_152 = 153:-1, 154:1 b_153 = 154:-1, 155:1 b_154 = 155:-1, 156:1 b_155 = 156:-1, 157:1 b_156 = 157:-1, 158:1 b_157 = 158:-1, 159:1 b_158 = 159:-1, 160:1 b_159 = 160:-1, 161:1 b_160 = 161:-1, 162:1 b_161 = 162:-1, 163:1 b_162 = 163:-1, 164:1 b_163 = 164:-1, 165:1 b_164 = 165:-1, 166:1 b_165 = 166:-1, 167:1 b_166 = 167:-1, 168:1 b_167 = 168:-1, 169:1 b_168 = 169:-1, 170:1 b_169 = 170:-1, 171:1 b_170 = 171:-1, 172:1 b_171 = 172:-1, 173:1 b_172 = 173:-1, 174:1 b_173 = 174:-1, 175:1 b_174 = 175:-1, 176:1 b_175 = 176:-1, 177:1 b_176 = 177:-1, 178:1 b_177 = 178:-1, 179:1 b_178 = 179:-1, 180:1 b_179 = 180:-1, 181:1 b_180 = 181:-1, 182:1 b_181 = 182:-1, 183:1 b_182 = 183:-1, 184:1 b_183 = 184:1708, 185:1 b_184 = 184:-1328, 186:1
Download: conway-lattice-D184-gram.txt
192904128 0 0 0 0 0 0 0 0 36 11 -3 0 0 0 0 0 11 6 -4 1 0 0 0 0 -3 -4 6 -4 1 0 0 0 0 1 -4 6 -4 1 0 0 0 0 1 -4 6 -4 1 0 0 0 0 1 -4 6 -4 0 0 0 0 0 1 -4 6
Shown above: the upper-left 8×8 block. The full Gram matrix is in the text file.
Download: conway-lattice-D184.sage