Properties

Label 108.4.h
Level 108
Weight 4
Character orbit h
Rep. character \(\chi_{108}(35,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 32
Newform subspaces 2
Sturm bound 72
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(108, [\chi])\).

Total New Old
Modular forms 120 40 80
Cusp forms 96 32 64
Eisenstein series 24 8 16

Trace form

\( 32q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 32q + 3q^{2} - q^{4} + 6q^{5} - 20q^{10} - 2q^{13} + 78q^{14} - q^{16} + 234q^{20} + 15q^{22} + 198q^{25} - 132q^{28} - 78q^{29} - 687q^{32} - 191q^{34} - 8q^{37} - 891q^{38} + 34q^{40} + 156q^{41} + 48q^{46} + 194q^{49} + 1977q^{50} - 332q^{52} + 3006q^{56} - 314q^{58} - 2q^{61} + 410q^{64} - 690q^{65} - 4845q^{68} + 84q^{70} - 836q^{73} - 5874q^{74} - 495q^{76} - 978q^{77} + 682q^{82} + 248q^{85} + 8331q^{86} + 531q^{88} + 8724q^{92} + 168q^{94} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.4.h.a \(8\) \(6.372\) 8.0.\(\cdots\).1 None \(3\) \(0\) \(-66\) \(0\) \(q+\beta _{7}q^{2}+(2\beta _{2}-2\beta _{3}-2\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
108.4.h.b \(24\) \(6.372\) None \(0\) \(0\) \(72\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 3 T - T^{2} + 12 T^{3} - 24 T^{4} + 96 T^{5} - 64 T^{6} - 1536 T^{7} + 4096 T^{8} \))
$3$ 1
$5$ (\( ( 1 + 33 T + 683 T^{2} + 10560 T^{3} + 132150 T^{4} + 1320000 T^{5} + 10671875 T^{6} + 64453125 T^{7} + 244140625 T^{8} )^{2} \))
$7$ (\( 1 + 763 T^{2} + 286549 T^{4} + 46025686 T^{6} + 5058296518 T^{8} + 5414875932214 T^{10} + 3966207006159349 T^{12} + 1242479575205672587 T^{14} + \)\(19\!\cdots\!01\)\( T^{16} \))
$11$ (\( 1 - 3248 T^{2} + 5235775 T^{4} - 5750931536 T^{6} + 6408197652976 T^{8} - 10188126022847696 T^{10} + 16432104834126393775 T^{12} - \)\(18\!\cdots\!88\)\( T^{14} + \)\(98\!\cdots\!41\)\( T^{16} \))
$13$ (\( ( 1 - 107 T + 4255 T^{2} - 299600 T^{3} + 21773374 T^{4} - 658221200 T^{5} + 20538072295 T^{6} - 1134681432911 T^{7} + 23298085122481 T^{8} )^{2} \))
$17$ (\( ( 1 - 9325 T^{2} + 46774812 T^{4} - 225082830925 T^{6} + 582622237229761 T^{8} )^{2} \))
$19$ (\( ( 1 + 239 T^{2} + 51737136 T^{4} + 11243965559 T^{6} + 2213314919066161 T^{8} )^{2} \))
$23$ (\( 1 - 37877 T^{2} + 781967941 T^{4} - 13507976408570 T^{6} + 191719381723246342 T^{8} - \)\(19\!\cdots\!30\)\( T^{10} + \)\(17\!\cdots\!61\)\( T^{12} - \)\(12\!\cdots\!13\)\( T^{14} + \)\(48\!\cdots\!41\)\( T^{16} \))
$29$ (\( ( 1 - 249 T + 63635 T^{2} - 10699032 T^{3} + 1755473166 T^{4} - 260938691448 T^{5} + 37851582031835 T^{6} - 3612279347991381 T^{7} + 353814783205469041 T^{8} )^{2} \))
$31$ (\( 1 + 72991 T^{2} + 2479562881 T^{4} + 78327798131458 T^{6} + 2595801970489726078 T^{8} + \)\(69\!\cdots\!98\)\( T^{10} + \)\(19\!\cdots\!41\)\( T^{12} + \)\(51\!\cdots\!31\)\( T^{14} + \)\(62\!\cdots\!21\)\( T^{16} \))
$37$ (\( ( 1 + 314 T + 125706 T^{2} + 15905042 T^{3} + 2565726409 T^{4} )^{4} \))
$41$ (\( ( 1 - 636 T + 254507 T^{2} - 76113300 T^{3} + 18864757656 T^{4} - 5245804749300 T^{5} + 1208934780064187 T^{6} - 208214910274559196 T^{7} + 22563490300366186081 T^{8} )^{2} \))
$43$ (\( 1 + 261520 T^{2} + 39141940543 T^{4} + 4343335603853680 T^{6} + \)\(38\!\cdots\!48\)\( T^{8} + \)\(27\!\cdots\!20\)\( T^{10} + \)\(15\!\cdots\!43\)\( T^{12} + \)\(66\!\cdots\!80\)\( T^{14} + \)\(15\!\cdots\!01\)\( T^{16} \))
$47$ (\( 1 - 58493 T^{2} - 17900011739 T^{4} + 13862131479910 T^{6} + \)\(30\!\cdots\!82\)\( T^{8} + \)\(14\!\cdots\!90\)\( T^{10} - \)\(20\!\cdots\!99\)\( T^{12} - \)\(73\!\cdots\!77\)\( T^{14} + \)\(13\!\cdots\!81\)\( T^{16} \))
$53$ (\( ( 1 - 363880 T^{2} + 76436876862 T^{4} - 8065167727620520 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} )^{2} \))
$59$ (\( 1 - 717032 T^{2} + 302479462375 T^{4} - 91274129085638744 T^{6} + \)\(21\!\cdots\!36\)\( T^{8} - \)\(38\!\cdots\!04\)\( T^{10} + \)\(53\!\cdots\!75\)\( T^{12} - \)\(53\!\cdots\!72\)\( T^{14} + \)\(31\!\cdots\!61\)\( T^{16} \))
$61$ (\( ( 1 - 131 T - 127289 T^{2} + 40546072 T^{3} - 34549792802 T^{4} + 9203187968632 T^{5} - 6557976932037329 T^{6} - 1531933138161272471 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} )^{2} \))
$67$ (\( 1 + 1070656 T^{2} + 683126750095 T^{4} + 302204171872082368 T^{6} + \)\(10\!\cdots\!36\)\( T^{8} + \)\(27\!\cdots\!92\)\( T^{10} + \)\(55\!\cdots\!95\)\( T^{12} + \)\(79\!\cdots\!04\)\( T^{14} + \)\(66\!\cdots\!21\)\( T^{16} \))
$71$ (\( ( 1 + 1260428 T^{2} + 653321166774 T^{4} + 161461184661978188 T^{6} + \)\(16\!\cdots\!41\)\( T^{8} )^{2} \))
$73$ (\( ( 1 - 985 T + 570834 T^{2} - 383181745 T^{3} + 151334226289 T^{4} )^{4} \))
$79$ (\( 1 + 259483 T^{2} - 289013191643 T^{4} - 33688753687579130 T^{6} + \)\(51\!\cdots\!14\)\( T^{8} - \)\(81\!\cdots\!30\)\( T^{10} - \)\(17\!\cdots\!63\)\( T^{12} + \)\(37\!\cdots\!63\)\( T^{14} + \)\(34\!\cdots\!81\)\( T^{16} \))
$83$ (\( 1 - 1120157 T^{2} + 290685528061 T^{4} - 347456380544486450 T^{6} + \)\(41\!\cdots\!02\)\( T^{8} - \)\(11\!\cdots\!50\)\( T^{10} + \)\(31\!\cdots\!21\)\( T^{12} - \)\(39\!\cdots\!13\)\( T^{14} + \)\(11\!\cdots\!21\)\( T^{16} \))
$89$ (\( ( 1 - 2694616 T^{2} + 2805913145742 T^{4} - 1339173738324165976 T^{6} + \)\(24\!\cdots\!21\)\( T^{8} )^{2} \))
$97$ (\( ( 1 + 286 T - 1237115 T^{2} - 144840410 T^{3} + 831901220284 T^{4} - 132191931515930 T^{5} - 1030482161877739835 T^{6} + \)\(21\!\cdots\!62\)\( T^{7} + \)\(69\!\cdots\!41\)\( T^{8} )^{2} \))
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