Properties

Label 108.5.g
Level 108
Weight 5
Character orbit g
Rep. character \(\chi_{108}(17,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 8
Newform subspaces 1
Sturm bound 90
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(108, [\chi])\).

Total New Old
Modular forms 162 8 154
Cusp forms 126 8 118
Eisenstein series 36 0 36

Trace form

\( 8q + 9q^{5} + 13q^{7} + O(q^{10}) \) \( 8q + 9q^{5} + 13q^{7} + 18q^{11} - 5q^{13} + 562q^{19} + 1719q^{23} + 353q^{25} - 2115q^{29} + 187q^{31} + 16q^{37} + 7920q^{41} - 68q^{43} - 13689q^{47} - 327q^{49} - 1818q^{55} + 20052q^{59} - 1937q^{61} - 25965q^{65} + 154q^{67} - 7802q^{73} + 25641q^{77} - 2195q^{79} - 37017q^{83} - 3042q^{85} + 15830q^{91} + 37116q^{95} + 7282q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.5.g.a \(8\) \(11.164\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(9\) \(13\) \(q+(2+\beta _{2}+\beta _{4}+\beta _{7})q^{5}+(3-\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( 1 - 9 T + 1114 T^{2} - 9783 T^{3} + 533599 T^{4} - 10528056 T^{5} + 59806456 T^{6} - 10305069192 T^{7} - 6001445444 T^{8} - 6440668245000 T^{9} + 23361896875000 T^{10} - 2570326171875000 T^{11} + 81420745849609375 T^{12} - 932979583740234375 T^{13} + 66399574279785156250 T^{14} - \)\(33\!\cdots\!25\)\( T^{15} + \)\(23\!\cdots\!25\)\( T^{16} \)
$7$ \( 1 - 13 T - 4554 T^{2} + 124753 T^{3} + 8962391 T^{4} - 347580324 T^{5} + 2901735784 T^{6} + 447642835484 T^{7} - 30706182623268 T^{8} + 1074790447997084 T^{9} + 16727929349338984 T^{10} - 4810959089900633124 T^{11} + \)\(29\!\cdots\!91\)\( T^{12} + \)\(99\!\cdots\!53\)\( T^{13} - \)\(87\!\cdots\!54\)\( T^{14} - \)\(59\!\cdots\!13\)\( T^{15} + \)\(11\!\cdots\!01\)\( T^{16} \)
$11$ \( 1 - 18 T + 33850 T^{2} - 607356 T^{3} + 452208721 T^{4} - 17443950048 T^{5} + 9074477968558 T^{6} - 445095012639474 T^{7} + 191968264536523468 T^{8} - 6516636080054538834 T^{9} + \)\(19\!\cdots\!98\)\( T^{10} - \)\(54\!\cdots\!08\)\( T^{11} + \)\(20\!\cdots\!81\)\( T^{12} - \)\(40\!\cdots\!56\)\( T^{13} + \)\(33\!\cdots\!50\)\( T^{14} - \)\(25\!\cdots\!58\)\( T^{15} + \)\(21\!\cdots\!21\)\( T^{16} \)
$13$ \( 1 + 5 T - 42054 T^{2} - 7266665 T^{3} + 352176575 T^{4} + 250092029040 T^{5} + 23191943061904 T^{6} - 3464858176098460 T^{7} - 548440340475170196 T^{8} - 98959814367548116060 T^{9} + \)\(18\!\cdots\!84\)\( T^{10} + \)\(58\!\cdots\!40\)\( T^{11} + \)\(23\!\cdots\!75\)\( T^{12} - \)\(13\!\cdots\!65\)\( T^{13} - \)\(22\!\cdots\!94\)\( T^{14} + \)\(77\!\cdots\!05\)\( T^{15} + \)\(44\!\cdots\!81\)\( T^{16} \)
$17$ \( 1 - 288125 T^{2} + 52320681154 T^{4} - 6759733382202755 T^{6} + \)\(63\!\cdots\!86\)\( T^{8} - \)\(47\!\cdots\!55\)\( T^{10} + \)\(25\!\cdots\!74\)\( T^{12} - \)\(97\!\cdots\!25\)\( T^{14} + \)\(23\!\cdots\!61\)\( T^{16} \)
$19$ \( ( 1 - 281 T + 110170 T^{2} + 68843041 T^{3} - 21846246566 T^{4} + 8971693946161 T^{5} + 1871079140226970 T^{6} - 621941492257591241 T^{7} + \)\(28\!\cdots\!81\)\( T^{8} )^{2} \)
$23$ \( 1 - 1719 T + 1529458 T^{2} - 935945649 T^{3} + 342642958747 T^{4} + 16333135609500 T^{5} - 118516645434237428 T^{6} + \)\(10\!\cdots\!68\)\( T^{7} - \)\(65\!\cdots\!00\)\( T^{8} + \)\(29\!\cdots\!88\)\( T^{9} - \)\(92\!\cdots\!68\)\( T^{10} + \)\(35\!\cdots\!00\)\( T^{11} + \)\(21\!\cdots\!67\)\( T^{12} - \)\(16\!\cdots\!49\)\( T^{13} + \)\(73\!\cdots\!78\)\( T^{14} - \)\(23\!\cdots\!39\)\( T^{15} + \)\(37\!\cdots\!21\)\( T^{16} \)
$29$ \( 1 + 2115 T + 4091014 T^{2} + 5498870985 T^{3} + 7048695081595 T^{4} + 8024737206821040 T^{5} + 8297140249856169556 T^{6} + \)\(79\!\cdots\!80\)\( T^{7} + \)\(68\!\cdots\!24\)\( T^{8} + \)\(56\!\cdots\!80\)\( T^{9} + \)\(41\!\cdots\!16\)\( T^{10} + \)\(28\!\cdots\!40\)\( T^{11} + \)\(17\!\cdots\!95\)\( T^{12} + \)\(97\!\cdots\!85\)\( T^{13} + \)\(51\!\cdots\!34\)\( T^{14} + \)\(18\!\cdots\!15\)\( T^{15} + \)\(62\!\cdots\!41\)\( T^{16} \)
$31$ \( 1 - 187 T - 2516004 T^{2} + 186847537 T^{3} + 3362431719041 T^{4} - 296059350096 T^{5} - 3460282108678916846 T^{6} - 13487262715981377034 T^{7} + \)\(31\!\cdots\!92\)\( T^{8} - \)\(12\!\cdots\!14\)\( T^{9} - \)\(29\!\cdots\!86\)\( T^{10} - \)\(23\!\cdots\!56\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} + \)\(12\!\cdots\!37\)\( T^{13} - \)\(15\!\cdots\!84\)\( T^{14} - \)\(10\!\cdots\!67\)\( T^{15} + \)\(52\!\cdots\!61\)\( T^{16} \)
$37$ \( ( 1 - 8 T + 3611368 T^{2} + 1256575624 T^{3} + 6911619203950 T^{4} + 2355025028051464 T^{5} + 12684855900547773928 T^{6} - 52663616046720282248 T^{7} + \)\(12\!\cdots\!41\)\( T^{8} )^{2} \)
$41$ \( 1 - 7920 T + 37687894 T^{2} - 132890424480 T^{3} + 385083705354505 T^{4} - 963185727644706960 T^{5} + \)\(21\!\cdots\!66\)\( T^{6} - \)\(41\!\cdots\!20\)\( T^{7} + \)\(74\!\cdots\!64\)\( T^{8} - \)\(11\!\cdots\!20\)\( T^{9} + \)\(16\!\cdots\!86\)\( T^{10} - \)\(21\!\cdots\!60\)\( T^{11} + \)\(24\!\cdots\!05\)\( T^{12} - \)\(23\!\cdots\!80\)\( T^{13} + \)\(19\!\cdots\!34\)\( T^{14} - \)\(11\!\cdots\!20\)\( T^{15} + \)\(40\!\cdots\!81\)\( T^{16} \)
$43$ \( 1 + 68 T - 12950604 T^{2} - 209786648 T^{3} + 102574547445791 T^{4} + 59145034173804 T^{5} - \)\(54\!\cdots\!36\)\( T^{6} + \)\(27\!\cdots\!16\)\( T^{7} + \)\(21\!\cdots\!12\)\( T^{8} + \)\(94\!\cdots\!16\)\( T^{9} - \)\(63\!\cdots\!36\)\( T^{10} + \)\(23\!\cdots\!04\)\( T^{11} + \)\(14\!\cdots\!91\)\( T^{12} - \)\(97\!\cdots\!48\)\( T^{13} - \)\(20\!\cdots\!04\)\( T^{14} + \)\(37\!\cdots\!68\)\( T^{15} + \)\(18\!\cdots\!01\)\( T^{16} \)
$47$ \( 1 + 13689 T + 103685338 T^{2} + 564293857959 T^{3} + 2435028217967227 T^{4} + 8736748337842042500 T^{5} + \)\(26\!\cdots\!72\)\( T^{6} + \)\(71\!\cdots\!32\)\( T^{7} + \)\(16\!\cdots\!20\)\( T^{8} + \)\(35\!\cdots\!92\)\( T^{9} + \)\(63\!\cdots\!92\)\( T^{10} + \)\(10\!\cdots\!00\)\( T^{11} + \)\(13\!\cdots\!67\)\( T^{12} + \)\(15\!\cdots\!59\)\( T^{13} + \)\(13\!\cdots\!78\)\( T^{14} + \)\(90\!\cdots\!29\)\( T^{15} + \)\(32\!\cdots\!41\)\( T^{16} \)
$53$ \( 1 - 5145920 T^{2} + 115452291970684 T^{4} - 84051566001475463360 T^{6} + \)\(67\!\cdots\!26\)\( T^{8} - \)\(52\!\cdots\!60\)\( T^{10} + \)\(44\!\cdots\!64\)\( T^{12} - \)\(12\!\cdots\!20\)\( T^{14} + \)\(15\!\cdots\!41\)\( T^{16} \)
$59$ \( 1 - 20052 T + 216711700 T^{2} - 1657982214864 T^{3} + 9931594296358591 T^{4} - 49579528565018409012 T^{5} + \)\(21\!\cdots\!48\)\( T^{6} - \)\(84\!\cdots\!76\)\( T^{7} + \)\(30\!\cdots\!08\)\( T^{8} - \)\(10\!\cdots\!36\)\( T^{9} + \)\(31\!\cdots\!08\)\( T^{10} - \)\(88\!\cdots\!72\)\( T^{11} + \)\(21\!\cdots\!31\)\( T^{12} - \)\(43\!\cdots\!64\)\( T^{13} + \)\(68\!\cdots\!00\)\( T^{14} - \)\(76\!\cdots\!92\)\( T^{15} + \)\(46\!\cdots\!81\)\( T^{16} \)
$61$ \( 1 + 1937 T - 10529634 T^{2} + 149647181023 T^{3} + 416288373490931 T^{4} - 1350680282380662864 T^{5} + \)\(12\!\cdots\!24\)\( T^{6} + \)\(40\!\cdots\!44\)\( T^{7} - \)\(98\!\cdots\!68\)\( T^{8} + \)\(55\!\cdots\!04\)\( T^{9} + \)\(23\!\cdots\!44\)\( T^{10} - \)\(35\!\cdots\!44\)\( T^{11} + \)\(15\!\cdots\!91\)\( T^{12} + \)\(76\!\cdots\!23\)\( T^{13} - \)\(74\!\cdots\!94\)\( T^{14} + \)\(18\!\cdots\!97\)\( T^{15} + \)\(13\!\cdots\!21\)\( T^{16} \)
$67$ \( 1 - 154 T - 33835854 T^{2} - 25606229228 T^{3} + 539365905411977 T^{4} + 738160924156362336 T^{5} + \)\(70\!\cdots\!02\)\( T^{6} - \)\(11\!\cdots\!78\)\( T^{7} - \)\(26\!\cdots\!64\)\( T^{8} - \)\(22\!\cdots\!38\)\( T^{9} + \)\(28\!\cdots\!82\)\( T^{10} + \)\(60\!\cdots\!96\)\( T^{11} + \)\(88\!\cdots\!37\)\( T^{12} - \)\(85\!\cdots\!28\)\( T^{13} - \)\(22\!\cdots\!34\)\( T^{14} - \)\(20\!\cdots\!14\)\( T^{15} + \)\(27\!\cdots\!61\)\( T^{16} \)
$71$ \( 1 - 68871716 T^{2} + 3244147638477940 T^{4} - \)\(11\!\cdots\!24\)\( T^{6} + \)\(30\!\cdots\!74\)\( T^{8} - \)\(73\!\cdots\!64\)\( T^{10} + \)\(13\!\cdots\!40\)\( T^{12} - \)\(18\!\cdots\!96\)\( T^{14} + \)\(17\!\cdots\!41\)\( T^{16} \)
$73$ \( ( 1 + 3901 T + 59309470 T^{2} + 292589317519 T^{3} + 2279602007321194 T^{4} + 8309021952930084079 T^{5} + \)\(47\!\cdots\!70\)\( T^{6} + \)\(89\!\cdots\!21\)\( T^{7} + \)\(65\!\cdots\!61\)\( T^{8} )^{2} \)
$79$ \( 1 + 2195 T - 87724914 T^{2} - 187644610415 T^{3} + 3128319215246375 T^{4} + 3711455091635884260 T^{5} - \)\(16\!\cdots\!36\)\( T^{6} + \)\(76\!\cdots\!80\)\( T^{7} + \)\(88\!\cdots\!64\)\( T^{8} + \)\(29\!\cdots\!80\)\( T^{9} - \)\(24\!\cdots\!96\)\( T^{10} + \)\(21\!\cdots\!60\)\( T^{11} + \)\(72\!\cdots\!75\)\( T^{12} - \)\(16\!\cdots\!15\)\( T^{13} - \)\(30\!\cdots\!34\)\( T^{14} + \)\(29\!\cdots\!95\)\( T^{15} + \)\(52\!\cdots\!41\)\( T^{16} \)
$83$ \( 1 + 37017 T + 725723290 T^{2} + 9956481997959 T^{3} + 104510585134438411 T^{4} + \)\(87\!\cdots\!72\)\( T^{5} + \)\(62\!\cdots\!28\)\( T^{6} + \)\(40\!\cdots\!76\)\( T^{7} + \)\(26\!\cdots\!48\)\( T^{8} + \)\(19\!\cdots\!96\)\( T^{9} + \)\(14\!\cdots\!48\)\( T^{10} + \)\(93\!\cdots\!92\)\( T^{11} + \)\(53\!\cdots\!91\)\( T^{12} + \)\(23\!\cdots\!59\)\( T^{13} + \)\(82\!\cdots\!90\)\( T^{14} + \)\(20\!\cdots\!97\)\( T^{15} + \)\(25\!\cdots\!61\)\( T^{16} \)
$89$ \( 1 - 294759296 T^{2} + 46567064448316540 T^{4} - \)\(48\!\cdots\!04\)\( T^{6} + \)\(35\!\cdots\!14\)\( T^{8} - \)\(19\!\cdots\!24\)\( T^{10} + \)\(72\!\cdots\!40\)\( T^{12} - \)\(17\!\cdots\!36\)\( T^{14} + \)\(24\!\cdots\!21\)\( T^{16} \)
$97$ \( 1 - 7282 T - 283226964 T^{2} + 993163976152 T^{3} + 57034963146137471 T^{4} - 97460573991801682656 T^{5} - \)\(75\!\cdots\!16\)\( T^{6} + \)\(33\!\cdots\!26\)\( T^{7} + \)\(75\!\cdots\!52\)\( T^{8} + \)\(29\!\cdots\!06\)\( T^{9} - \)\(58\!\cdots\!76\)\( T^{10} - \)\(67\!\cdots\!96\)\( T^{11} + \)\(35\!\cdots\!91\)\( T^{12} + \)\(54\!\cdots\!52\)\( T^{13} - \)\(13\!\cdots\!84\)\( T^{14} - \)\(31\!\cdots\!02\)\( T^{15} + \)\(37\!\cdots\!41\)\( T^{16} \)
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