Properties

Label 105.4.d
Level 105
Weight 4
Character orbit d
Rep. character \(\chi_{105}(64,\cdot)\)
Character field \(\Q\)
Dimension 16
Newform subspaces 2
Sturm bound 64
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

Trace form

\( 16q - 60q^{4} - 28q^{5} - 12q^{6} - 144q^{9} + O(q^{10}) \) \( 16q - 60q^{4} - 28q^{5} - 12q^{6} - 144q^{9} + 8q^{10} - 24q^{15} + 172q^{16} - 72q^{19} + 700q^{20} - 84q^{21} + 324q^{24} - 8q^{25} + 696q^{26} - 1080q^{29} - 432q^{30} - 48q^{31} - 152q^{34} + 56q^{35} + 540q^{36} + 600q^{39} - 2144q^{40} + 1192q^{41} + 32q^{44} + 252q^{45} - 64q^{46} - 784q^{49} - 1288q^{50} - 1560q^{51} + 108q^{54} + 1408q^{55} + 168q^{56} + 352q^{59} - 228q^{60} - 440q^{61} + 1476q^{64} - 3312q^{65} + 1920q^{66} - 1776q^{69} - 756q^{70} + 904q^{71} + 664q^{74} + 528q^{75} + 7840q^{76} + 4880q^{79} - 332q^{80} + 1296q^{81} + 1008q^{84} - 1272q^{85} - 4200q^{86} + 3304q^{89} - 72q^{90} - 1456q^{91} - 9304q^{94} + 440q^{95} + 1236q^{96} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.4.d.a \(6\) \(6.195\) 6.0.84052224.1 None \(0\) \(0\) \(-14\) \(0\) \(q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
105.4.d.b \(10\) \(6.195\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-14\) \(0\) \(q+\beta _{6}q^{2}-3\beta _{2}q^{3}+(-5-\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 21 T^{2} + 267 T^{4} - 2607 T^{6} + 17088 T^{8} - 86016 T^{10} + 262144 T^{12} \))(\( 1 - 13 T^{2} + 115 T^{4} - 1151 T^{6} + 11968 T^{8} - 114560 T^{10} + 765952 T^{12} - 4714496 T^{14} + 30146560 T^{16} - 218103808 T^{18} + 1073741824 T^{20} \))
$3$ (\( ( 1 + 9 T^{2} )^{3} \))(\( ( 1 + 9 T^{2} )^{5} \))
$5$ (\( 1 + 14 T - 85 T^{2} - 2700 T^{3} - 10625 T^{4} + 218750 T^{5} + 1953125 T^{6} \))(\( 1 + 14 T + 285 T^{2} + 1152 T^{3} + 2830 T^{4} - 184700 T^{5} + 353750 T^{6} + 18000000 T^{7} + 556640625 T^{8} + 3417968750 T^{9} + 30517578125 T^{10} \))
$7$ (\( ( 1 + 49 T^{2} )^{3} \))(\( ( 1 + 49 T^{2} )^{5} \))
$11$ (\( ( 1 + 66 T + 3717 T^{2} + 169572 T^{3} + 4947327 T^{4} + 116923026 T^{5} + 2357947691 T^{6} )^{2} \))(\( ( 1 - 66 T + 4555 T^{2} - 210928 T^{3} + 10802758 T^{4} - 383496700 T^{5} + 14378470898 T^{6} - 373671818608 T^{7} + 10740451732505 T^{8} - 207136272863586 T^{9} + 4177248169415651 T^{10} )^{2} \))
$13$ (\( 1 - 8946 T^{2} + 38833239 T^{4} - 104657523868 T^{6} + 187440627504351 T^{8} - 208424669505715026 T^{10} + \)\(11\!\cdots\!29\)\( T^{12} \))(\( 1 - 13662 T^{2} + 97034245 T^{4} - 454371436584 T^{6} + 1533415610487218 T^{8} - 3873561618402720820 T^{10} + \)\(74\!\cdots\!62\)\( T^{12} - \)\(10\!\cdots\!04\)\( T^{14} + \)\(10\!\cdots\!05\)\( T^{16} - \)\(74\!\cdots\!82\)\( T^{18} + \)\(26\!\cdots\!49\)\( T^{20} \))
$17$ (\( 1 - 18630 T^{2} + 165676335 T^{4} - 961084533780 T^{6} + 3999023967729615 T^{8} - 10854252279590447430 T^{10} + \)\(14\!\cdots\!09\)\( T^{12} \))(\( 1 - 3586 T^{2} - 9840163 T^{4} - 226703927544 T^{6} + 917313320435074 T^{8} + 2772044023815717620 T^{10} + \)\(22\!\cdots\!06\)\( T^{12} - \)\(13\!\cdots\!84\)\( T^{14} - \)\(13\!\cdots\!67\)\( T^{16} - \)\(12\!\cdots\!06\)\( T^{18} + \)\(81\!\cdots\!49\)\( T^{20} \))
$19$ (\( ( 1 - 138 T + 26205 T^{2} - 1963716 T^{3} + 179740095 T^{4} - 6492331578 T^{5} + 322687697779 T^{6} )^{2} \))(\( ( 1 + 174 T + 30655 T^{2} + 3260120 T^{3} + 355132498 T^{4} + 29134734196 T^{5} + 2435853803782 T^{6} + 153375217565720 T^{7} + 9891991375415245 T^{8} + 385116795917512014 T^{9} + 15181127029874798299 T^{10} )^{2} \))
$23$ (\( 1 - 48042 T^{2} + 1101997215 T^{4} - 16142068432204 T^{6} + 163135137398049135 T^{8} - \)\(10\!\cdots\!82\)\( T^{10} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 - 68862 T^{2} + 2443463533 T^{4} - 58952757931656 T^{6} + 1054996500313105346 T^{8} - \)\(14\!\cdots\!64\)\( T^{10} + \)\(15\!\cdots\!94\)\( T^{12} - \)\(12\!\cdots\!76\)\( T^{14} + \)\(79\!\cdots\!77\)\( T^{16} - \)\(33\!\cdots\!42\)\( T^{18} + \)\(71\!\cdots\!49\)\( T^{20} \))
$29$ (\( ( 1 + 170 T + 65051 T^{2} + 6611676 T^{3} + 1586528839 T^{4} + 101119964570 T^{5} + 14507145975869 T^{6} )^{2} \))(\( ( 1 + 370 T + 160385 T^{2} + 37125560 T^{3} + 8745786530 T^{4} + 1370740158092 T^{5} + 213300987680170 T^{6} + 22083148893184760 T^{7} + 2326728607339749565 T^{8} + \)\(13\!\cdots\!70\)\( T^{9} + \)\(86\!\cdots\!49\)\( T^{10} )^{2} \))
$31$ (\( ( 1 + 366 T + 102201 T^{2} + 18296380 T^{3} + 3044669991 T^{4} + 324826347246 T^{5} + 26439622160671 T^{6} )^{2} \))(\( ( 1 - 342 T + 142051 T^{2} - 26927448 T^{3} + 6639779138 T^{4} - 944601593732 T^{5} + 197805660300158 T^{6} - 23898209219936088 T^{7} + 3755774767545476221 T^{8} - \)\(26\!\cdots\!62\)\( T^{9} + \)\(23\!\cdots\!51\)\( T^{10} )^{2} \))
$37$ (\( 1 - 135294 T^{2} + 11227035399 T^{4} - 635435307878212 T^{6} + 28805501217992152191 T^{8} - \)\(89\!\cdots\!14\)\( T^{10} + \)\(16\!\cdots\!29\)\( T^{12} \))(\( 1 - 160866 T^{2} + 14645741397 T^{4} - 941454249392984 T^{6} + 51314852590450172274 T^{8} - \)\(26\!\cdots\!00\)\( T^{10} + \)\(13\!\cdots\!66\)\( T^{12} - \)\(61\!\cdots\!04\)\( T^{14} + \)\(24\!\cdots\!13\)\( T^{16} - \)\(69\!\cdots\!26\)\( T^{18} + \)\(11\!\cdots\!49\)\( T^{20} \))
$41$ (\( ( 1 + 206 T + 68783 T^{2} + 10173252 T^{3} + 4740593143 T^{4} + 978521473646 T^{5} + 327381934393961 T^{6} )^{2} \))(\( ( 1 - 802 T + 392457 T^{2} - 146273472 T^{3} + 44792512462 T^{4} - 12012058617212 T^{5} + 3087144751393502 T^{6} - 694814239692994752 T^{7} + \)\(12\!\cdots\!77\)\( T^{8} - \)\(18\!\cdots\!62\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} )^{2} \))
$43$ (\( 1 - 142146 T^{2} + 11474416359 T^{4} - 844942679855548 T^{6} + 72533951580623718591 T^{8} - \)\(56\!\cdots\!46\)\( T^{10} + \)\(25\!\cdots\!49\)\( T^{12} \))(\( 1 - 485758 T^{2} + 119488561781 T^{4} - 19372440245362728 T^{6} + \)\(22\!\cdots\!22\)\( T^{8} - \)\(20\!\cdots\!28\)\( T^{10} + \)\(14\!\cdots\!78\)\( T^{12} - \)\(77\!\cdots\!28\)\( T^{14} + \)\(30\!\cdots\!69\)\( T^{16} - \)\(77\!\cdots\!58\)\( T^{18} + \)\(10\!\cdots\!49\)\( T^{20} \))
$47$ (\( 1 - 167706 T^{2} + 23309138223 T^{4} - 3026280208385068 T^{6} + \)\(25\!\cdots\!67\)\( T^{8} - \)\(19\!\cdots\!46\)\( T^{10} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 - 502182 T^{2} + 138597263629 T^{4} - 26712508734207432 T^{6} + \)\(39\!\cdots\!54\)\( T^{8} - \)\(45\!\cdots\!76\)\( T^{10} + \)\(42\!\cdots\!66\)\( T^{12} - \)\(31\!\cdots\!12\)\( T^{14} + \)\(17\!\cdots\!81\)\( T^{16} - \)\(67\!\cdots\!42\)\( T^{18} + \)\(14\!\cdots\!49\)\( T^{20} \))
$53$ (\( 1 - 466338 T^{2} + 138876104679 T^{4} - 24411867787298428 T^{6} + \)\(30\!\cdots\!91\)\( T^{8} - \)\(22\!\cdots\!58\)\( T^{10} + \)\(10\!\cdots\!89\)\( T^{12} \))(\( 1 - 997006 T^{2} + 484698335029 T^{4} - 151727963326781416 T^{6} + \)\(34\!\cdots\!38\)\( T^{8} - \)\(57\!\cdots\!36\)\( T^{10} + \)\(75\!\cdots\!02\)\( T^{12} - \)\(74\!\cdots\!56\)\( T^{14} + \)\(52\!\cdots\!81\)\( T^{16} - \)\(24\!\cdots\!86\)\( T^{18} + \)\(53\!\cdots\!49\)\( T^{20} \))
$59$ (\( ( 1 - 880 T + 706697 T^{2} - 338588064 T^{3} + 145140723163 T^{4} - 37118869604080 T^{5} + 8662995818654939 T^{6} )^{2} \))(\( ( 1 + 704 T + 427487 T^{2} + 197865856 T^{3} + 99740405354 T^{4} + 55609053370240 T^{5} + 20484584711199166 T^{6} + 8346087395413261696 T^{7} + \)\(37\!\cdots\!93\)\( T^{8} + \)\(12\!\cdots\!24\)\( T^{9} + \)\(36\!\cdots\!99\)\( T^{10} )^{2} \))
$61$ (\( ( 1 + 870 T + 582363 T^{2} + 282478148 T^{3} + 132185336103 T^{4} + 44822725694070 T^{5} + 11694146092834141 T^{6} )^{2} \))(\( ( 1 - 650 T + 689345 T^{2} - 375251480 T^{3} + 259020342850 T^{4} - 102268282520348 T^{5} + 58792696440435850 T^{6} - 19333096729119304280 T^{7} + \)\(80\!\cdots\!45\)\( T^{8} - \)\(17\!\cdots\!50\)\( T^{9} + \)\(60\!\cdots\!01\)\( T^{10} )^{2} \))
$67$ (\( 1 - 1101858 T^{2} + 638460439095 T^{4} - 237880710542256316 T^{6} + \)\(57\!\cdots\!55\)\( T^{8} - \)\(90\!\cdots\!38\)\( T^{10} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( 1 - 2016990 T^{2} + 1931325978405 T^{4} - 1175831601966849320 T^{6} + \)\(51\!\cdots\!30\)\( T^{8} - \)\(17\!\cdots\!32\)\( T^{10} + \)\(46\!\cdots\!70\)\( T^{12} - \)\(96\!\cdots\!20\)\( T^{14} + \)\(14\!\cdots\!45\)\( T^{16} - \)\(13\!\cdots\!90\)\( T^{18} + \)\(60\!\cdots\!49\)\( T^{20} \))
$71$ (\( ( 1 + 1018 T + 1108049 T^{2} + 595462884 T^{3} + 396582925639 T^{4} + 130406089031578 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 - 1470 T + 1881615 T^{2} - 1727909680 T^{3} + 1338943951990 T^{4} - 860023408325220 T^{5} + 479222768800692890 T^{6} - \)\(22\!\cdots\!80\)\( T^{7} + \)\(86\!\cdots\!65\)\( T^{8} - \)\(24\!\cdots\!70\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{2} \))
$73$ (\( 1 - 596010 T^{2} + 300446924511 T^{4} - 131249091840782924 T^{6} + \)\(45\!\cdots\!79\)\( T^{8} - \)\(13\!\cdots\!10\)\( T^{10} + \)\(34\!\cdots\!69\)\( T^{12} \))(\( 1 - 2398886 T^{2} + 2442762516189 T^{4} - 1366613667006822216 T^{6} + \)\(48\!\cdots\!38\)\( T^{8} - \)\(16\!\cdots\!36\)\( T^{10} + \)\(73\!\cdots\!82\)\( T^{12} - \)\(31\!\cdots\!36\)\( T^{14} + \)\(84\!\cdots\!41\)\( T^{16} - \)\(12\!\cdots\!26\)\( T^{18} + \)\(79\!\cdots\!49\)\( T^{20} \))
$79$ (\( ( 1 - 1620 T + 1787517 T^{2} - 1338821912 T^{3} + 881315594163 T^{4} - 393801677944020 T^{5} + 119851595982618319 T^{6} )^{2} \))(\( ( 1 - 820 T + 1736795 T^{2} - 1027136240 T^{3} + 1389341527610 T^{4} - 657402503393464 T^{5} + 684999557431306790 T^{6} - \)\(24\!\cdots\!40\)\( T^{7} + \)\(20\!\cdots\!05\)\( T^{8} - \)\(48\!\cdots\!20\)\( T^{9} + \)\(29\!\cdots\!99\)\( T^{10} )^{2} \))
$83$ (\( 1 - 1086594 T^{2} + 1370317231383 T^{4} - 756582920323766652 T^{6} + \)\(44\!\cdots\!27\)\( T^{8} - \)\(11\!\cdots\!34\)\( T^{10} + \)\(34\!\cdots\!09\)\( T^{12} \))(\( 1 - 4743150 T^{2} + 10500593430085 T^{4} - 14340896860193237480 T^{6} + \)\(13\!\cdots\!10\)\( T^{8} - \)\(90\!\cdots\!28\)\( T^{10} + \)\(43\!\cdots\!90\)\( T^{12} - \)\(15\!\cdots\!80\)\( T^{14} + \)\(36\!\cdots\!65\)\( T^{16} - \)\(54\!\cdots\!50\)\( T^{18} + \)\(37\!\cdots\!49\)\( T^{20} \))
$89$ (\( ( 1 - 1938 T + 3246255 T^{2} - 2913932892 T^{3} + 2288509141095 T^{4} - 963149741882418 T^{5} + 350356403707485209 T^{6} )^{2} \))(\( ( 1 + 286 T + 2177465 T^{2} + 600135040 T^{3} + 2162009088238 T^{4} + 560754412921604 T^{5} + 1524149384926054622 T^{6} + \)\(29\!\cdots\!40\)\( T^{7} + \)\(76\!\cdots\!85\)\( T^{8} + \)\(70\!\cdots\!06\)\( T^{9} + \)\(17\!\cdots\!49\)\( T^{10} )^{2} \))
$97$ (\( 1 - 3336954 T^{2} + 5694689958159 T^{4} - 6336320517980710252 T^{6} + \)\(47\!\cdots\!11\)\( T^{8} - \)\(23\!\cdots\!14\)\( T^{10} + \)\(57\!\cdots\!89\)\( T^{12} \))(\( 1 - 6782134 T^{2} + 21944276999789 T^{4} - 44851979434890226824 T^{6} + \)\(64\!\cdots\!18\)\( T^{8} - \)\(68\!\cdots\!04\)\( T^{10} + \)\(53\!\cdots\!22\)\( T^{12} - \)\(31\!\cdots\!84\)\( T^{14} + \)\(12\!\cdots\!21\)\( T^{16} - \)\(32\!\cdots\!54\)\( T^{18} + \)\(40\!\cdots\!49\)\( T^{20} \))
show more
show less