Properties

Label 24.8.d
Level 24
Weight 8
Character orbit d
Rep. character \(\chi_{24}(13,\cdot)\)
Character field \(\Q\)
Dimension 14
Newform subspaces 1
Sturm bound 32
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 24.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(24, [\chi])\).

Total New Old
Modular forms 30 14 16
Cusp forms 26 14 12
Eisenstein series 4 0 4

Trace form

\( 14q - 14q^{2} - 208q^{4} - 54q^{6} + 1372q^{7} - 428q^{8} - 10206q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 208q^{4} - 54q^{6} + 1372q^{7} - 428q^{8} - 10206q^{9} + 5020q^{10} + 7668q^{12} + 4636q^{14} - 13500q^{15} - 43336q^{16} - 2908q^{17} + 10206q^{18} + 175096q^{20} - 128480q^{22} - 143416q^{23} - 29268q^{24} - 202626q^{25} + 424984q^{26} + 567520q^{28} - 250668q^{30} - 89468q^{31} - 893944q^{32} + 1109820q^{34} + 151632q^{36} - 823816q^{38} + 474552q^{39} - 860888q^{40} - 441284q^{41} + 427788q^{42} + 1275264q^{44} - 2167992q^{46} - 1056408q^{47} - 233280q^{48} + 2158134q^{49} + 324610q^{50} - 2059248q^{52} + 39366q^{54} + 4757504q^{55} + 1643704q^{56} + 1551096q^{57} - 5494676q^{58} - 3203712q^{60} + 5767172q^{62} - 1000188q^{63} + 3852224q^{64} - 2520464q^{65} - 3615840q^{66} - 3735840q^{68} + 12890312q^{70} + 5172696q^{71} + 312012q^{72} - 5446196q^{73} - 6468800q^{74} - 9084624q^{76} + 3542184q^{78} - 14373548q^{79} + 14369088q^{80} + 7440174q^{81} - 7935708q^{82} - 2775816q^{84} + 4738312q^{86} + 7902036q^{87} + 12598720q^{88} - 11952620q^{89} - 3659580q^{90} + 11004480q^{92} - 15440088q^{94} - 69327376q^{95} + 1341576q^{96} + 133732q^{97} + 53030538q^{98} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.8.d.a \(14\) \(7.497\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(0\) \(0\) \(1372\) \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(-15-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 14 T + 202 T^{2} + 2056 T^{3} + 30032 T^{4} + 487040 T^{5} + 5227008 T^{6} + 74227712 T^{7} + 669057024 T^{8} + 7979663360 T^{9} + 62981668864 T^{10} + 551903297536 T^{11} + 6940667150336 T^{12} + 61572651155456 T^{13} + 562949953421312 T^{14} \)
$3$ \( ( 1 + 729 T^{2} )^{7} \)
$5$ \( 1 - 445562 T^{2} + 95581517971 T^{4} - 14439744600730244 T^{6} + \)\(18\!\cdots\!25\)\( T^{8} - \)\(20\!\cdots\!50\)\( T^{10} + \)\(19\!\cdots\!75\)\( T^{12} - \)\(15\!\cdots\!00\)\( T^{14} + \)\(11\!\cdots\!75\)\( T^{16} - \)\(76\!\cdots\!50\)\( T^{18} + \)\(41\!\cdots\!25\)\( T^{20} - \)\(20\!\cdots\!00\)\( T^{22} + \)\(80\!\cdots\!75\)\( T^{24} - \)\(23\!\cdots\!50\)\( T^{26} + \)\(31\!\cdots\!25\)\( T^{28} \)
$7$ \( ( 1 - 686 T + 2578165 T^{2} - 1521968292 T^{3} + 2893978871217 T^{4} - 1670463194093586 T^{5} + 2150164822127173261 T^{6} - \)\(14\!\cdots\!28\)\( T^{7} + \)\(17\!\cdots\!23\)\( T^{8} - \)\(11\!\cdots\!14\)\( T^{9} + \)\(16\!\cdots\!19\)\( T^{10} - \)\(70\!\cdots\!92\)\( T^{11} + \)\(97\!\cdots\!95\)\( T^{12} - \)\(21\!\cdots\!14\)\( T^{13} + \)\(25\!\cdots\!07\)\( T^{14} )^{2} \)
$11$ \( 1 - 126612650 T^{2} + 7858670884605619 T^{4} - \)\(31\!\cdots\!48\)\( T^{6} + \)\(91\!\cdots\!17\)\( T^{8} - \)\(20\!\cdots\!90\)\( T^{10} + \)\(40\!\cdots\!27\)\( T^{12} - \)\(76\!\cdots\!72\)\( T^{14} + \)\(15\!\cdots\!07\)\( T^{16} - \)\(29\!\cdots\!90\)\( T^{18} + \)\(50\!\cdots\!57\)\( T^{20} - \)\(65\!\cdots\!28\)\( T^{22} + \)\(62\!\cdots\!19\)\( T^{24} - \)\(37\!\cdots\!50\)\( T^{26} + \)\(11\!\cdots\!81\)\( T^{28} \)
$13$ \( 1 - 387011990 T^{2} + 68908126519682275 T^{4} - \)\(76\!\cdots\!28\)\( T^{6} + \)\(63\!\cdots\!97\)\( T^{8} - \)\(48\!\cdots\!86\)\( T^{10} + \)\(37\!\cdots\!83\)\( T^{12} - \)\(25\!\cdots\!72\)\( T^{14} + \)\(14\!\cdots\!87\)\( T^{16} - \)\(75\!\cdots\!06\)\( T^{18} + \)\(38\!\cdots\!93\)\( T^{20} - \)\(18\!\cdots\!48\)\( T^{22} + \)\(65\!\cdots\!75\)\( T^{24} - \)\(14\!\cdots\!90\)\( T^{26} + \)\(14\!\cdots\!29\)\( T^{28} \)
$17$ \( ( 1 + 1454 T + 1716640747 T^{2} + 5874996114796 T^{3} + 1576054531620987017 T^{4} + \)\(56\!\cdots\!70\)\( T^{5} + \)\(93\!\cdots\!91\)\( T^{6} + \)\(30\!\cdots\!24\)\( T^{7} + \)\(38\!\cdots\!43\)\( T^{8} + \)\(95\!\cdots\!30\)\( T^{9} + \)\(10\!\cdots\!89\)\( T^{10} + \)\(16\!\cdots\!36\)\( T^{11} + \)\(19\!\cdots\!71\)\( T^{12} + \)\(69\!\cdots\!06\)\( T^{13} + \)\(19\!\cdots\!97\)\( T^{14} )^{2} \)
$19$ \( 1 - 6974011850 T^{2} + 24092658824990296867 T^{4} - \)\(55\!\cdots\!68\)\( T^{6} + \)\(96\!\cdots\!09\)\( T^{8} - \)\(13\!\cdots\!10\)\( T^{10} + \)\(15\!\cdots\!79\)\( T^{12} - \)\(15\!\cdots\!56\)\( T^{14} + \)\(12\!\cdots\!59\)\( T^{16} - \)\(85\!\cdots\!10\)\( T^{18} + \)\(49\!\cdots\!49\)\( T^{20} - \)\(22\!\cdots\!08\)\( T^{22} + \)\(78\!\cdots\!67\)\( T^{24} - \)\(18\!\cdots\!50\)\( T^{26} + \)\(20\!\cdots\!41\)\( T^{28} \)
$23$ \( ( 1 + 71708 T + 8440179361 T^{2} + 617221190675032 T^{3} + 59565824725230322613 T^{4} + \)\(38\!\cdots\!00\)\( T^{5} + \)\(26\!\cdots\!93\)\( T^{6} + \)\(15\!\cdots\!24\)\( T^{7} + \)\(90\!\cdots\!71\)\( T^{8} + \)\(44\!\cdots\!00\)\( T^{9} + \)\(23\!\cdots\!99\)\( T^{10} + \)\(82\!\cdots\!92\)\( T^{11} + \)\(38\!\cdots\!27\)\( T^{12} + \)\(11\!\cdots\!32\)\( T^{13} + \)\(53\!\cdots\!63\)\( T^{14} )^{2} \)
$29$ \( 1 - 131972594954 T^{2} + \)\(90\!\cdots\!15\)\( T^{4} - \)\(42\!\cdots\!72\)\( T^{6} + \)\(15\!\cdots\!49\)\( T^{8} - \)\(42\!\cdots\!06\)\( T^{10} + \)\(96\!\cdots\!91\)\( T^{12} - \)\(18\!\cdots\!28\)\( T^{14} + \)\(28\!\cdots\!71\)\( T^{16} - \)\(37\!\cdots\!66\)\( T^{18} + \)\(39\!\cdots\!09\)\( T^{20} - \)\(33\!\cdots\!12\)\( T^{22} + \)\(21\!\cdots\!15\)\( T^{24} - \)\(91\!\cdots\!74\)\( T^{26} + \)\(20\!\cdots\!61\)\( T^{28} \)
$31$ \( ( 1 + 44734 T + 103891511821 T^{2} + 1878217501397540 T^{3} + \)\(54\!\cdots\!97\)\( T^{4} - \)\(16\!\cdots\!38\)\( T^{5} + \)\(19\!\cdots\!65\)\( T^{6} - \)\(22\!\cdots\!20\)\( T^{7} + \)\(53\!\cdots\!15\)\( T^{8} - \)\(12\!\cdots\!98\)\( T^{9} + \)\(11\!\cdots\!07\)\( T^{10} + \)\(10\!\cdots\!40\)\( T^{11} + \)\(16\!\cdots\!71\)\( T^{12} + \)\(19\!\cdots\!74\)\( T^{13} + \)\(11\!\cdots\!71\)\( T^{14} )^{2} \)
$37$ \( 1 - 856038434294 T^{2} + \)\(35\!\cdots\!75\)\( T^{4} - \)\(98\!\cdots\!16\)\( T^{6} + \)\(19\!\cdots\!85\)\( T^{8} - \)\(31\!\cdots\!86\)\( T^{10} + \)\(39\!\cdots\!27\)\( T^{12} - \)\(41\!\cdots\!48\)\( T^{14} + \)\(35\!\cdots\!03\)\( T^{16} - \)\(25\!\cdots\!06\)\( T^{18} + \)\(14\!\cdots\!65\)\( T^{20} - \)\(64\!\cdots\!56\)\( T^{22} + \)\(21\!\cdots\!75\)\( T^{24} - \)\(45\!\cdots\!34\)\( T^{26} + \)\(48\!\cdots\!29\)\( T^{28} \)
$41$ \( ( 1 + 220642 T + 805010558083 T^{2} + 256070152586388116 T^{3} + \)\(34\!\cdots\!41\)\( T^{4} + \)\(10\!\cdots\!18\)\( T^{5} + \)\(99\!\cdots\!91\)\( T^{6} + \)\(26\!\cdots\!36\)\( T^{7} + \)\(19\!\cdots\!71\)\( T^{8} + \)\(41\!\cdots\!98\)\( T^{9} + \)\(25\!\cdots\!81\)\( T^{10} + \)\(36\!\cdots\!36\)\( T^{11} + \)\(22\!\cdots\!83\)\( T^{12} + \)\(12\!\cdots\!02\)\( T^{13} + \)\(10\!\cdots\!61\)\( T^{14} )^{2} \)
$43$ \( 1 - 1167136384250 T^{2} + \)\(84\!\cdots\!19\)\( T^{4} - \)\(44\!\cdots\!04\)\( T^{6} + \)\(19\!\cdots\!85\)\( T^{8} - \)\(71\!\cdots\!86\)\( T^{10} + \)\(23\!\cdots\!47\)\( T^{12} - \)\(67\!\cdots\!20\)\( T^{14} + \)\(17\!\cdots\!03\)\( T^{16} - \)\(39\!\cdots\!86\)\( T^{18} + \)\(77\!\cdots\!65\)\( T^{20} - \)\(13\!\cdots\!04\)\( T^{22} + \)\(18\!\cdots\!31\)\( T^{24} - \)\(18\!\cdots\!50\)\( T^{26} + \)\(12\!\cdots\!49\)\( T^{28} \)
$47$ \( ( 1 + 528204 T + 1304181982841 T^{2} + 1396775026647992952 T^{3} + \)\(11\!\cdots\!01\)\( T^{4} + \)\(11\!\cdots\!48\)\( T^{5} + \)\(10\!\cdots\!97\)\( T^{6} + \)\(58\!\cdots\!04\)\( T^{7} + \)\(51\!\cdots\!11\)\( T^{8} + \)\(29\!\cdots\!12\)\( T^{9} + \)\(15\!\cdots\!47\)\( T^{10} + \)\(92\!\cdots\!72\)\( T^{11} + \)\(43\!\cdots\!63\)\( T^{12} + \)\(89\!\cdots\!36\)\( T^{13} + \)\(85\!\cdots\!67\)\( T^{14} )^{2} \)
$53$ \( 1 - 6871654175354 T^{2} + \)\(23\!\cdots\!55\)\( T^{4} - \)\(56\!\cdots\!16\)\( T^{6} + \)\(10\!\cdots\!25\)\( T^{8} - \)\(16\!\cdots\!86\)\( T^{10} + \)\(23\!\cdots\!07\)\( T^{12} - \)\(30\!\cdots\!88\)\( T^{14} + \)\(33\!\cdots\!83\)\( T^{16} - \)\(32\!\cdots\!46\)\( T^{18} + \)\(27\!\cdots\!25\)\( T^{20} - \)\(20\!\cdots\!36\)\( T^{22} + \)\(11\!\cdots\!95\)\( T^{24} - \)\(47\!\cdots\!74\)\( T^{26} + \)\(95\!\cdots\!89\)\( T^{28} \)
$59$ \( 1 - 9783224696858 T^{2} + \)\(58\!\cdots\!71\)\( T^{4} - \)\(24\!\cdots\!08\)\( T^{6} + \)\(78\!\cdots\!05\)\( T^{8} - \)\(20\!\cdots\!62\)\( T^{10} + \)\(47\!\cdots\!59\)\( T^{12} - \)\(11\!\cdots\!36\)\( T^{14} + \)\(29\!\cdots\!99\)\( T^{16} - \)\(78\!\cdots\!02\)\( T^{18} + \)\(18\!\cdots\!05\)\( T^{20} - \)\(35\!\cdots\!28\)\( T^{22} + \)\(53\!\cdots\!71\)\( T^{24} - \)\(55\!\cdots\!38\)\( T^{26} + \)\(34\!\cdots\!21\)\( T^{28} \)
$61$ \( 1 - 26713863605222 T^{2} + \)\(33\!\cdots\!19\)\( T^{4} - \)\(26\!\cdots\!04\)\( T^{6} + \)\(14\!\cdots\!33\)\( T^{8} - \)\(67\!\cdots\!58\)\( T^{10} + \)\(25\!\cdots\!03\)\( T^{12} - \)\(83\!\cdots\!44\)\( T^{14} + \)\(24\!\cdots\!23\)\( T^{16} - \)\(65\!\cdots\!98\)\( T^{18} + \)\(14\!\cdots\!93\)\( T^{20} - \)\(25\!\cdots\!44\)\( T^{22} + \)\(31\!\cdots\!19\)\( T^{24} - \)\(24\!\cdots\!02\)\( T^{26} + \)\(91\!\cdots\!81\)\( T^{28} \)
$67$ \( 1 - 42926594518442 T^{2} + \)\(97\!\cdots\!99\)\( T^{4} - \)\(14\!\cdots\!60\)\( T^{6} + \)\(17\!\cdots\!33\)\( T^{8} - \)\(16\!\cdots\!82\)\( T^{10} + \)\(12\!\cdots\!95\)\( T^{12} - \)\(81\!\cdots\!52\)\( T^{14} + \)\(45\!\cdots\!55\)\( T^{16} - \)\(21\!\cdots\!62\)\( T^{18} + \)\(86\!\cdots\!37\)\( T^{20} - \)\(27\!\cdots\!60\)\( T^{22} + \)\(65\!\cdots\!51\)\( T^{24} - \)\(10\!\cdots\!82\)\( T^{26} + \)\(90\!\cdots\!09\)\( T^{28} \)
$71$ \( ( 1 - 2586348 T + 45775649603153 T^{2} - \)\(10\!\cdots\!00\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} - \)\(21\!\cdots\!72\)\( T^{5} + \)\(14\!\cdots\!09\)\( T^{6} - \)\(24\!\cdots\!88\)\( T^{7} + \)\(13\!\cdots\!19\)\( T^{8} - \)\(17\!\cdots\!32\)\( T^{9} + \)\(78\!\cdots\!91\)\( T^{10} - \)\(75\!\cdots\!00\)\( T^{11} + \)\(28\!\cdots\!03\)\( T^{12} - \)\(14\!\cdots\!68\)\( T^{13} + \)\(51\!\cdots\!31\)\( T^{14} )^{2} \)
$73$ \( ( 1 + 2723098 T + 38312704682563 T^{2} + 83515159987399400068 T^{3} + \)\(83\!\cdots\!09\)\( T^{4} + \)\(14\!\cdots\!06\)\( T^{5} + \)\(12\!\cdots\!59\)\( T^{6} + \)\(19\!\cdots\!00\)\( T^{7} + \)\(13\!\cdots\!23\)\( T^{8} + \)\(17\!\cdots\!54\)\( T^{9} + \)\(11\!\cdots\!57\)\( T^{10} + \)\(12\!\cdots\!08\)\( T^{11} + \)\(63\!\cdots\!91\)\( T^{12} + \)\(49\!\cdots\!42\)\( T^{13} + \)\(20\!\cdots\!13\)\( T^{14} )^{2} \)
$79$ \( ( 1 + 7186774 T + 105650603277469 T^{2} + \)\(49\!\cdots\!68\)\( T^{3} + \)\(43\!\cdots\!13\)\( T^{4} + \)\(14\!\cdots\!10\)\( T^{5} + \)\(10\!\cdots\!25\)\( T^{6} + \)\(30\!\cdots\!36\)\( T^{7} + \)\(20\!\cdots\!75\)\( T^{8} + \)\(55\!\cdots\!10\)\( T^{9} + \)\(30\!\cdots\!27\)\( T^{10} + \)\(67\!\cdots\!48\)\( T^{11} + \)\(27\!\cdots\!31\)\( T^{12} + \)\(36\!\cdots\!34\)\( T^{13} + \)\(96\!\cdots\!19\)\( T^{14} )^{2} \)
$83$ \( 1 - 148527772994618 T^{2} + \)\(11\!\cdots\!55\)\( T^{4} - \)\(65\!\cdots\!68\)\( T^{6} + \)\(28\!\cdots\!13\)\( T^{8} - \)\(10\!\cdots\!42\)\( T^{10} + \)\(33\!\cdots\!55\)\( T^{12} - \)\(95\!\cdots\!24\)\( T^{14} + \)\(24\!\cdots\!95\)\( T^{16} - \)\(56\!\cdots\!22\)\( T^{18} + \)\(11\!\cdots\!57\)\( T^{20} - \)\(19\!\cdots\!08\)\( T^{22} + \)\(25\!\cdots\!95\)\( T^{24} - \)\(23\!\cdots\!78\)\( T^{26} + \)\(11\!\cdots\!09\)\( T^{28} \)
$89$ \( ( 1 + 5976310 T + 88567149413395 T^{2} + \)\(34\!\cdots\!52\)\( T^{3} + \)\(24\!\cdots\!97\)\( T^{4} - \)\(58\!\cdots\!66\)\( T^{5} - \)\(32\!\cdots\!17\)\( T^{6} - \)\(90\!\cdots\!92\)\( T^{7} - \)\(14\!\cdots\!93\)\( T^{8} - \)\(11\!\cdots\!06\)\( T^{9} + \)\(20\!\cdots\!33\)\( T^{10} + \)\(13\!\cdots\!12\)\( T^{11} + \)\(14\!\cdots\!55\)\( T^{12} + \)\(44\!\cdots\!10\)\( T^{13} + \)\(33\!\cdots\!09\)\( T^{14} )^{2} \)
$97$ \( ( 1 - 66866 T + 239738062759867 T^{2} - 35467286602626108564 T^{3} + \)\(36\!\cdots\!25\)\( T^{4} + \)\(10\!\cdots\!02\)\( T^{5} + \)\(38\!\cdots\!03\)\( T^{6} + \)\(18\!\cdots\!76\)\( T^{7} + \)\(30\!\cdots\!39\)\( T^{8} + \)\(67\!\cdots\!38\)\( T^{9} + \)\(19\!\cdots\!25\)\( T^{10} - \)\(15\!\cdots\!04\)\( T^{11} + \)\(82\!\cdots\!31\)\( T^{12} - \)\(18\!\cdots\!94\)\( T^{13} + \)\(22\!\cdots\!17\)\( T^{14} )^{2} \)
show more
show less