Properties

Label 105.3.h
Level 105
Weight 3
Character orbit h
Rep. character \(\chi_{105}(76,\cdot)\)
Character field \(\Q\)
Dimension 12
Newform subspaces 1
Sturm bound 48
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(105, [\chi])\).

Total New Old
Modular forms 36 12 24
Cusp forms 28 12 16
Eisenstein series 8 0 8

Trace form

\( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10}) \) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} - 16q^{11} - 40q^{14} + 92q^{16} + 12q^{18} + 36q^{21} - 88q^{22} - 64q^{23} - 60q^{25} + 88q^{28} + 104q^{29} - 228q^{32} + 60q^{35} - 132q^{36} + 32q^{37} - 24q^{39} - 60q^{42} + 152q^{43} + 192q^{44} + 200q^{46} + 60q^{49} + 20q^{50} + 24q^{51} + 176q^{53} - 368q^{56} - 240q^{57} - 400q^{58} + 24q^{63} - 20q^{64} - 240q^{65} + 168q^{67} - 60q^{70} + 32q^{71} - 12q^{72} + 184q^{74} + 8q^{77} + 456q^{78} + 120q^{79} + 108q^{81} + 108q^{84} + 120q^{85} + 400q^{86} - 536q^{88} + 24q^{91} + 192q^{92} + 48q^{93} + 884q^{98} + 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.3.h.a \(12\) \(2.861\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(0\) \(0\) \(-8\) \(q+\beta _{4}q^{2}-\beta _{3}q^{3}+(4-\beta _{1})q^{4}+\beta _{8}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + 2 T + 3 T^{2} + 7 T^{4} + 38 T^{5} + 109 T^{6} + 152 T^{7} + 112 T^{8} + 768 T^{10} + 2048 T^{11} + 4096 T^{12} )^{2} \)
$3$ \( ( 1 + 3 T^{2} )^{6} \)
$5$ \( ( 1 + 5 T^{2} )^{6} \)
$7$ \( 1 + 8 T + 2 T^{2} + 312 T^{3} + 4255 T^{4} + 13888 T^{5} + 43708 T^{6} + 680512 T^{7} + 10216255 T^{8} + 36706488 T^{9} + 11529602 T^{10} + 2259801992 T^{11} + 13841287201 T^{12} \)
$11$ \( ( 1 + 8 T + 198 T^{2} + 1416 T^{3} + 30895 T^{4} + 264944 T^{5} + 5610292 T^{6} + 32058224 T^{7} + 452333695 T^{8} + 2508530376 T^{9} + 42443058438 T^{10} + 207499396808 T^{11} + 3138428376721 T^{12} )^{2} \)
$13$ \( 1 - 852 T^{2} + 436674 T^{4} - 159409348 T^{6} + 45042421839 T^{8} - 10253858128680 T^{10} + 1907667001388316 T^{12} - 292860442013229480 T^{14} + 36742487242313615919 T^{16} - \)\(37\!\cdots\!88\)\( T^{18} + \)\(29\!\cdots\!34\)\( T^{20} - \)\(16\!\cdots\!52\)\( T^{22} + \)\(54\!\cdots\!61\)\( T^{24} \)
$17$ \( 1 - 2172 T^{2} + 2401794 T^{4} - 1757595148 T^{6} + 941667483759 T^{8} - 387997181982840 T^{10} + 125896935467491356 T^{12} - 32405912636388779640 T^{14} + \)\(65\!\cdots\!19\)\( T^{16} - \)\(10\!\cdots\!28\)\( T^{18} + \)\(11\!\cdots\!14\)\( T^{20} - \)\(88\!\cdots\!72\)\( T^{22} + \)\(33\!\cdots\!21\)\( T^{24} \)
$19$ \( 1 - 1404 T^{2} + 1342050 T^{4} - 896154316 T^{6} + 500154418383 T^{8} - 227690692547448 T^{10} + 90028611036772572 T^{12} - 29672878743475970808 T^{14} + \)\(84\!\cdots\!03\)\( T^{16} - \)\(19\!\cdots\!76\)\( T^{18} + \)\(38\!\cdots\!50\)\( T^{20} - \)\(52\!\cdots\!04\)\( T^{22} + \)\(48\!\cdots\!21\)\( T^{24} \)
$23$ \( ( 1 + 32 T + 2418 T^{2} + 60144 T^{3} + 2694751 T^{4} + 53735792 T^{5} + 1782680284 T^{6} + 28426233968 T^{7} + 754101814591 T^{8} + 8903470508016 T^{9} + 189355962409458 T^{10} + 1325648358836768 T^{11} + 21914624432020321 T^{12} )^{2} \)
$29$ \( ( 1 - 52 T + 3990 T^{2} - 132324 T^{3} + 6311983 T^{4} - 164304136 T^{5} + 6334525012 T^{6} - 138179778376 T^{7} + 4464345648223 T^{8} - 78709401128004 T^{9} + 1995983187714390 T^{10} - 21876776131610452 T^{11} + 353814783205469041 T^{12} )^{2} \)
$31$ \( 1 - 6228 T^{2} + 19622274 T^{4} - 42341564932 T^{6} + 69647410996719 T^{8} - 91080823295899560 T^{10} + 96735996796679061276 T^{12} - \)\(84\!\cdots\!60\)\( T^{14} + \)\(59\!\cdots\!79\)\( T^{16} - \)\(33\!\cdots\!52\)\( T^{18} + \)\(14\!\cdots\!94\)\( T^{20} - \)\(41\!\cdots\!28\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \)
$37$ \( ( 1 - 16 T + 4622 T^{2} + 32784 T^{3} + 7136719 T^{4} + 278279680 T^{5} + 7429424740 T^{6} + 380964881920 T^{7} + 13375360417759 T^{8} + 84114774592656 T^{9} + 16234680036022862 T^{10} - 76937349958685584 T^{11} + 6582952005840035281 T^{12} )^{2} \)
$41$ \( 1 - 7524 T^{2} + 32464386 T^{4} - 93240551380 T^{6} + 206850565610415 T^{8} - 379921653079011144 T^{10} + \)\(65\!\cdots\!56\)\( T^{12} - \)\(10\!\cdots\!84\)\( T^{14} + \)\(16\!\cdots\!15\)\( T^{16} - \)\(21\!\cdots\!80\)\( T^{18} + \)\(20\!\cdots\!26\)\( T^{20} - \)\(13\!\cdots\!24\)\( T^{22} + \)\(50\!\cdots\!61\)\( T^{24} \)
$43$ \( ( 1 - 76 T + 9590 T^{2} - 631788 T^{3} + 42146383 T^{4} - 2188827368 T^{5} + 102971644948 T^{6} - 4047141803432 T^{7} + 144090096346783 T^{8} - 3993761318001612 T^{9} + 112089840662193590 T^{10} - 1642472655809602924 T^{11} + 39959630797262576401 T^{12} )^{2} \)
$47$ \( 1 - 6132 T^{2} + 27456354 T^{4} - 92403901348 T^{6} + 277727516070639 T^{8} - 754801362269230440 T^{10} + \)\(17\!\cdots\!96\)\( T^{12} - \)\(36\!\cdots\!40\)\( T^{14} + \)\(66\!\cdots\!79\)\( T^{16} - \)\(10\!\cdots\!68\)\( T^{18} + \)\(15\!\cdots\!34\)\( T^{20} - \)\(16\!\cdots\!32\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \)
$53$ \( ( 1 - 88 T + 10434 T^{2} - 574440 T^{3} + 50272015 T^{4} - 2575931008 T^{5} + 181692199804 T^{6} - 7235790201472 T^{7} + 396670379189215 T^{8} - 12732095606942760 T^{9} + 649617609752140674 T^{10} - 15390097392165148312 T^{11} + \)\(49\!\cdots\!41\)\( T^{12} )^{2} \)
$59$ \( 1 - 15948 T^{2} + 137050242 T^{4} - 864152710108 T^{6} + 4419517662043791 T^{8} - 18954945757384385304 T^{10} + \)\(70\!\cdots\!16\)\( T^{12} - \)\(22\!\cdots\!44\)\( T^{14} + \)\(64\!\cdots\!11\)\( T^{16} - \)\(15\!\cdots\!48\)\( T^{18} + \)\(29\!\cdots\!22\)\( T^{20} - \)\(41\!\cdots\!48\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \)
$61$ \( 1 - 13716 T^{2} + 109224834 T^{4} - 648593370628 T^{6} + 3203041286245839 T^{8} - 13994290873734287016 T^{10} + \)\(55\!\cdots\!56\)\( T^{12} - \)\(19\!\cdots\!56\)\( T^{14} + \)\(61\!\cdots\!59\)\( T^{16} - \)\(17\!\cdots\!88\)\( T^{18} + \)\(40\!\cdots\!74\)\( T^{20} - \)\(69\!\cdots\!16\)\( T^{22} + \)\(70\!\cdots\!41\)\( T^{24} \)
$67$ \( ( 1 - 84 T + 15366 T^{2} - 763540 T^{3} + 102124911 T^{4} - 4033313976 T^{5} + 514098700788 T^{6} - 18105546438264 T^{7} + 2057931438675231 T^{8} - 69068593121318260 T^{9} + 6239635933335345606 T^{10} - \)\(15\!\cdots\!16\)\( T^{11} + \)\(81\!\cdots\!61\)\( T^{12} )^{2} \)
$71$ \( ( 1 - 16 T + 16698 T^{2} - 42336 T^{3} + 131112895 T^{4} + 1041328304 T^{5} + 716701578892 T^{6} + 5249335980464 T^{7} + 3331799062726495 T^{8} - 5423253620079456 T^{9} + 10782792464741717178 T^{10} - 52083896816158099216 T^{11} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \)
$73$ \( 1 - 19284 T^{2} + 216036930 T^{4} - 1973102936452 T^{6} + 14880325491672495 T^{8} - 96746229105564519336 T^{10} + \)\(55\!\cdots\!08\)\( T^{12} - \)\(27\!\cdots\!76\)\( T^{14} + \)\(12\!\cdots\!95\)\( T^{16} - \)\(45\!\cdots\!92\)\( T^{18} + \)\(14\!\cdots\!30\)\( T^{20} - \)\(35\!\cdots\!84\)\( T^{22} + \)\(52\!\cdots\!41\)\( T^{24} \)
$79$ \( ( 1 - 60 T + 22242 T^{2} - 662476 T^{3} + 201003183 T^{4} - 1192106616 T^{5} + 1261845815388 T^{6} - 7439937390456 T^{7} + 7829090259107823 T^{8} - 161039605183729996 T^{9} + 33743534149941729762 T^{10} - \)\(56\!\cdots\!60\)\( T^{11} + \)\(59\!\cdots\!41\)\( T^{12} )^{2} \)
$83$ \( 1 - 45420 T^{2} + 1066844514 T^{4} - 17098817034364 T^{6} + 206563644037003983 T^{8} - \)\(19\!\cdots\!08\)\( T^{10} + \)\(15\!\cdots\!04\)\( T^{12} - \)\(93\!\cdots\!68\)\( T^{14} + \)\(46\!\cdots\!03\)\( T^{16} - \)\(18\!\cdots\!04\)\( T^{18} + \)\(54\!\cdots\!34\)\( T^{20} - \)\(10\!\cdots\!20\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \)
$89$ \( 1 - 46020 T^{2} + 1126013634 T^{4} - 19221077499316 T^{6} + 252845241317038383 T^{8} - \)\(26\!\cdots\!72\)\( T^{10} + \)\(23\!\cdots\!84\)\( T^{12} - \)\(16\!\cdots\!52\)\( T^{14} + \)\(99\!\cdots\!23\)\( T^{16} - \)\(47\!\cdots\!36\)\( T^{18} + \)\(17\!\cdots\!74\)\( T^{20} - \)\(44\!\cdots\!20\)\( T^{22} + \)\(61\!\cdots\!41\)\( T^{24} \)
$97$ \( 1 - 51924 T^{2} + 1396974978 T^{4} - 26352399780484 T^{6} + 389015604150559215 T^{8} - \)\(47\!\cdots\!84\)\( T^{10} + \)\(48\!\cdots\!52\)\( T^{12} - \)\(41\!\cdots\!04\)\( T^{14} + \)\(30\!\cdots\!15\)\( T^{16} - \)\(18\!\cdots\!44\)\( T^{18} + \)\(85\!\cdots\!38\)\( T^{20} - \)\(28\!\cdots\!24\)\( T^{22} + \)\(48\!\cdots\!81\)\( T^{24} \)
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