Properties

Label 43.5.b
Level 43
Weight 5
Character orbit b
Rep. character \(\chi_{43}(42,\cdot)\)
Character field \(\Q\)
Dimension 13
Newform subspaces 2
Sturm bound 18
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(43, [\chi])\).

Total New Old
Modular forms 15 15 0
Cusp forms 13 13 0
Eisenstein series 2 2 0

Trace form

\( 13q - 76q^{4} + 126q^{6} - 381q^{9} + O(q^{10}) \) \( 13q - 76q^{4} + 126q^{6} - 381q^{9} + 182q^{10} + 19q^{11} - 265q^{13} + 732q^{14} - 92q^{15} + 1332q^{16} + 181q^{17} - 2392q^{21} + 517q^{23} - 4234q^{24} + 451q^{25} + 4149q^{31} + 936q^{35} + 5506q^{36} + 1242q^{38} - 2618q^{40} + 3037q^{41} + 741q^{43} - 11984q^{44} - 3860q^{47} - 6143q^{49} + 23300q^{52} - 437q^{53} - 10004q^{54} - 10152q^{56} - 7692q^{57} - 4666q^{58} + 9970q^{59} + 15848q^{60} - 11484q^{64} + 29808q^{66} - 1785q^{67} + 7234q^{68} - 7674q^{74} - 67708q^{78} + 12016q^{79} - 17099q^{81} - 5681q^{83} + 37180q^{84} - 14412q^{86} + 17850q^{87} + 4268q^{90} + 31570q^{92} + 606q^{95} + 50546q^{96} + 12589q^{97} - 9805q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.5.b.a \(1\) \(4.445\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{4}q^{4}+3^{4}q^{9}+199q^{11}-7^{2}q^{13}+\cdots\)
43.5.b.b \(12\) \(4.445\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-8+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 4 T )( 1 + 4 T ) \))(\( 1 - 50 T^{2} + 1349 T^{4} - 26056 T^{6} + 463232 T^{8} - 8751936 T^{10} + 150915312 T^{12} - 2240495616 T^{14} + 30358372352 T^{16} - 437147140096 T^{18} + 5793910882304 T^{20} - 54975581388800 T^{22} + 281474976710656 T^{24} \))
$3$ (\( ( 1 - 9 T )( 1 + 9 T ) \))(\( 1 - 255 T^{2} + 47783 T^{4} - 6646421 T^{6} + 799989903 T^{8} - 79711532676 T^{10} + 6990833564658 T^{12} - 522987365887236 T^{14} + 34436942157258063 T^{16} - 1877145602287584501 T^{18} + 88542863683907518503 T^{20} - \)\(31\!\cdots\!55\)\( T^{22} + \)\(79\!\cdots\!61\)\( T^{24} \))
$5$ (\( ( 1 - 25 T )( 1 + 25 T ) \))(\( 1 - 3663 T^{2} + 6511015 T^{4} - 7365160765 T^{6} + 5973224140031 T^{8} - 3902236317085676 T^{10} + 2399998678381934162 T^{12} - \)\(15\!\cdots\!00\)\( T^{14} + \)\(91\!\cdots\!75\)\( T^{16} - \)\(43\!\cdots\!25\)\( T^{18} + \)\(15\!\cdots\!75\)\( T^{20} - \)\(33\!\cdots\!75\)\( T^{22} + \)\(35\!\cdots\!25\)\( T^{24} \))
$7$ (\( ( 1 - 49 T )( 1 + 49 T ) \))(\( 1 - 10134 T^{2} + 60060006 T^{4} - 249160434566 T^{6} + 812915964019071 T^{8} - 2246049549704995236 T^{10} + \)\(56\!\cdots\!48\)\( T^{12} - \)\(12\!\cdots\!36\)\( T^{14} + \)\(27\!\cdots\!71\)\( T^{16} - \)\(47\!\cdots\!66\)\( T^{18} + \)\(66\!\cdots\!06\)\( T^{20} - \)\(64\!\cdots\!34\)\( T^{22} + \)\(36\!\cdots\!01\)\( T^{24} \))
$11$ (\( 1 - 199 T + 14641 T^{2} \))(\( ( 1 + 90 T + 69626 T^{2} + 4275732 T^{3} + 2084651350 T^{4} + 90865763142 T^{5} + 37469241503078 T^{6} + 1330365638162022 T^{7} + 446863530661139350 T^{8} + 13419078640054034772 T^{9} + \)\(31\!\cdots\!86\)\( T^{10} + \)\(60\!\cdots\!90\)\( T^{11} + \)\(98\!\cdots\!41\)\( T^{12} )^{2} \))
$13$ (\( 1 + 49 T + 28561 T^{2} \))(\( ( 1 + 108 T + 78130 T^{2} + 14124934 T^{3} + 3639591614 T^{4} + 705010114760 T^{5} + 121575713991590 T^{6} + 20135793887660360 T^{7} + 2968926691433773694 T^{8} + \)\(32\!\cdots\!54\)\( T^{9} + \)\(51\!\cdots\!30\)\( T^{10} + \)\(20\!\cdots\!08\)\( T^{11} + \)\(54\!\cdots\!61\)\( T^{12} )^{2} \))
$17$ (\( 1 + 497 T + 83521 T^{2} \))(\( ( 1 - 339 T + 345843 T^{2} - 103717833 T^{3} + 57770879546 T^{4} - 15179725016055 T^{5} + 6016834256618483 T^{6} - 1267825813065929655 T^{7} + \)\(40\!\cdots\!86\)\( T^{8} - \)\(60\!\cdots\!13\)\( T^{9} + \)\(16\!\cdots\!83\)\( T^{10} - \)\(13\!\cdots\!39\)\( T^{11} + \)\(33\!\cdots\!21\)\( T^{12} )^{2} \))
$19$ (\( ( 1 - 361 T )( 1 + 361 T ) \))(\( 1 - 1175657 T^{2} + 671010023409 T^{4} - 244979577528319381 T^{6} + \)\(63\!\cdots\!63\)\( T^{8} - \)\(12\!\cdots\!10\)\( T^{10} + \)\(18\!\cdots\!98\)\( T^{12} - \)\(20\!\cdots\!10\)\( T^{14} + \)\(18\!\cdots\!03\)\( T^{16} - \)\(12\!\cdots\!01\)\( T^{18} + \)\(55\!\cdots\!49\)\( T^{20} - \)\(16\!\cdots\!57\)\( T^{22} + \)\(23\!\cdots\!41\)\( T^{24} \))
$23$ (\( 1 + 1049 T + 279841 T^{2} \))(\( ( 1 - 783 T + 1163077 T^{2} - 843582057 T^{3} + 713091466102 T^{4} - 397049506101027 T^{5} + 259574077696956889 T^{6} - \)\(11\!\cdots\!07\)\( T^{7} + \)\(55\!\cdots\!62\)\( T^{8} - \)\(18\!\cdots\!97\)\( T^{9} + \)\(71\!\cdots\!97\)\( T^{10} - \)\(13\!\cdots\!83\)\( T^{11} + \)\(48\!\cdots\!41\)\( T^{12} )^{2} \))
$29$ (\( ( 1 - 841 T )( 1 + 841 T ) \))(\( 1 - 5231219 T^{2} + 13592412986871 T^{4} - 23367533349246758977 T^{6} + \)\(29\!\cdots\!35\)\( T^{8} - \)\(29\!\cdots\!88\)\( T^{10} + \)\(23\!\cdots\!82\)\( T^{12} - \)\(14\!\cdots\!68\)\( T^{14} + \)\(74\!\cdots\!35\)\( T^{16} - \)\(29\!\cdots\!37\)\( T^{18} + \)\(85\!\cdots\!11\)\( T^{20} - \)\(16\!\cdots\!19\)\( T^{22} + \)\(15\!\cdots\!61\)\( T^{24} \))
$31$ (\( 1 + 1561 T + 923521 T^{2} \))(\( ( 1 - 2855 T + 6518969 T^{2} - 8600011177 T^{3} + 10228398490358 T^{4} - 8682474860253963 T^{5} + 8850492205571119245 T^{6} - \)\(80\!\cdots\!23\)\( T^{7} + \)\(87\!\cdots\!78\)\( T^{8} - \)\(67\!\cdots\!97\)\( T^{9} + \)\(47\!\cdots\!89\)\( T^{10} - \)\(19\!\cdots\!55\)\( T^{11} + \)\(62\!\cdots\!21\)\( T^{12} )^{2} \))
$37$ (\( ( 1 - 1369 T )( 1 + 1369 T ) \))(\( 1 - 6978249 T^{2} + 25643197308697 T^{4} - 70260487375765593853 T^{6} + \)\(17\!\cdots\!59\)\( T^{8} - \)\(39\!\cdots\!70\)\( T^{10} + \)\(80\!\cdots\!70\)\( T^{12} - \)\(13\!\cdots\!70\)\( T^{14} + \)\(21\!\cdots\!19\)\( T^{16} - \)\(30\!\cdots\!33\)\( T^{18} + \)\(39\!\cdots\!57\)\( T^{20} - \)\(37\!\cdots\!49\)\( T^{22} + \)\(18\!\cdots\!21\)\( T^{24} \))
$41$ (\( 1 + 1841 T + 2825761 T^{2} \))(\( ( 1 - 2439 T + 13822603 T^{2} - 19943096547 T^{3} + 69051390319336 T^{4} - 65595635499999207 T^{5} + \)\(21\!\cdots\!21\)\( T^{6} - \)\(18\!\cdots\!27\)\( T^{7} + \)\(55\!\cdots\!56\)\( T^{8} - \)\(44\!\cdots\!07\)\( T^{9} + \)\(88\!\cdots\!23\)\( T^{10} - \)\(43\!\cdots\!39\)\( T^{11} + \)\(50\!\cdots\!61\)\( T^{12} )^{2} \))
$43$ (\( 1 - 1849 T \))(\( 1 + 1108 T + 1897246 T^{2} - 4681128092 T^{3} + 681017924063 T^{4} - 846563366867960 T^{5} + 64607141521498794692 T^{6} - \)\(28\!\cdots\!60\)\( T^{7} + \)\(79\!\cdots\!63\)\( T^{8} - \)\(18\!\cdots\!92\)\( T^{9} + \)\(25\!\cdots\!46\)\( T^{10} + \)\(51\!\cdots\!08\)\( T^{11} + \)\(15\!\cdots\!01\)\( T^{12} \))
$47$ (\( 1 - 1666 T + 4879681 T^{2} \))(\( ( 1 + 2763 T + 21754149 T^{2} + 55851382377 T^{3} + 234662825346711 T^{4} + 481604898621884868 T^{5} + \)\(14\!\cdots\!34\)\( T^{6} + \)\(23\!\cdots\!08\)\( T^{7} + \)\(55\!\cdots\!71\)\( T^{8} + \)\(64\!\cdots\!57\)\( T^{9} + \)\(12\!\cdots\!29\)\( T^{10} + \)\(76\!\cdots\!63\)\( T^{11} + \)\(13\!\cdots\!81\)\( T^{12} )^{2} \))
$53$ (\( 1 + 1649 T + 7890481 T^{2} \))(\( ( 1 - 606 T + 25718024 T^{2} - 24674633094 T^{3} + 346581142619392 T^{4} - 336085601563787574 T^{5} + \)\(32\!\cdots\!82\)\( T^{6} - \)\(26\!\cdots\!94\)\( T^{7} + \)\(21\!\cdots\!12\)\( T^{8} - \)\(12\!\cdots\!54\)\( T^{9} + \)\(99\!\cdots\!04\)\( T^{10} - \)\(18\!\cdots\!06\)\( T^{11} + \)\(24\!\cdots\!81\)\( T^{12} )^{2} \))
$59$ (\( 1 + 4046 T + 12117361 T^{2} \))(\( ( 1 - 7008 T + 80137258 T^{2} - 394451068512 T^{3} + 2532059909380847 T^{4} - 9247600606403540352 T^{5} + \)\(41\!\cdots\!80\)\( T^{6} - \)\(11\!\cdots\!72\)\( T^{7} + \)\(37\!\cdots\!87\)\( T^{8} - \)\(70\!\cdots\!72\)\( T^{9} + \)\(17\!\cdots\!78\)\( T^{10} - \)\(18\!\cdots\!08\)\( T^{11} + \)\(31\!\cdots\!61\)\( T^{12} )^{2} \))
$61$ (\( ( 1 - 3721 T )( 1 + 3721 T ) \))(\( 1 - 32665486 T^{2} + 1118892201421590 T^{4} - \)\(24\!\cdots\!14\)\( T^{6} + \)\(52\!\cdots\!07\)\( T^{8} - \)\(83\!\cdots\!88\)\( T^{10} + \)\(13\!\cdots\!08\)\( T^{12} - \)\(16\!\cdots\!28\)\( T^{14} + \)\(19\!\cdots\!27\)\( T^{16} - \)\(17\!\cdots\!74\)\( T^{18} + \)\(15\!\cdots\!90\)\( T^{20} - \)\(84\!\cdots\!86\)\( T^{22} + \)\(49\!\cdots\!81\)\( T^{24} \))
$67$ (\( 1 + 697 T + 20151121 T^{2} \))(\( ( 1 + 544 T + 66684038 T^{2} + 18315837698 T^{3} + 2452178722840730 T^{4} + 587634295199545788 T^{5} + \)\(60\!\cdots\!70\)\( T^{6} + \)\(11\!\cdots\!48\)\( T^{7} + \)\(99\!\cdots\!30\)\( T^{8} + \)\(14\!\cdots\!78\)\( T^{9} + \)\(10\!\cdots\!78\)\( T^{10} + \)\(18\!\cdots\!44\)\( T^{11} + \)\(66\!\cdots\!21\)\( T^{12} )^{2} \))
$71$ (\( ( 1 - 5041 T )( 1 + 5041 T ) \))(\( 1 - 101562020 T^{2} + 5784818387848562 T^{4} - \)\(20\!\cdots\!64\)\( T^{6} + \)\(47\!\cdots\!67\)\( T^{8} - \)\(75\!\cdots\!84\)\( T^{10} + \)\(13\!\cdots\!88\)\( T^{12} - \)\(48\!\cdots\!24\)\( T^{14} + \)\(20\!\cdots\!07\)\( T^{16} - \)\(54\!\cdots\!84\)\( T^{18} + \)\(10\!\cdots\!42\)\( T^{20} - \)\(11\!\cdots\!20\)\( T^{22} + \)\(72\!\cdots\!61\)\( T^{24} \))
$73$ (\( ( 1 - 5329 T )( 1 + 5329 T ) \))(\( 1 - 193491698 T^{2} + 19000747654703030 T^{4} - \)\(12\!\cdots\!18\)\( T^{6} + \)\(60\!\cdots\!75\)\( T^{8} - \)\(23\!\cdots\!56\)\( T^{10} + \)\(72\!\cdots\!44\)\( T^{12} - \)\(18\!\cdots\!36\)\( T^{14} + \)\(39\!\cdots\!75\)\( T^{16} - \)\(65\!\cdots\!38\)\( T^{18} + \)\(80\!\cdots\!30\)\( T^{20} - \)\(66\!\cdots\!98\)\( T^{22} + \)\(27\!\cdots\!81\)\( T^{24} \))
$79$ (\( 1 + 12286 T + 38950081 T^{2} \))(\( ( 1 - 12151 T + 155715789 T^{2} - 800821687889 T^{3} + 4128429862975343 T^{4} + 5685482156720652576 T^{5} - \)\(30\!\cdots\!42\)\( T^{6} + \)\(22\!\cdots\!56\)\( T^{7} + \)\(62\!\cdots\!23\)\( T^{8} - \)\(47\!\cdots\!49\)\( T^{9} + \)\(35\!\cdots\!69\)\( T^{10} - \)\(10\!\cdots\!51\)\( T^{11} + \)\(34\!\cdots\!81\)\( T^{12} )^{2} \))
$83$ (\( 1 - 1351 T + 47458321 T^{2} \))(\( ( 1 + 3516 T + 117162268 T^{2} + 863865543048 T^{3} + 7914887456622244 T^{4} + 75598926847021341108 T^{5} + \)\(40\!\cdots\!22\)\( T^{6} + \)\(35\!\cdots\!68\)\( T^{7} + \)\(17\!\cdots\!04\)\( T^{8} + \)\(92\!\cdots\!28\)\( T^{9} + \)\(59\!\cdots\!08\)\( T^{10} + \)\(84\!\cdots\!16\)\( T^{11} + \)\(11\!\cdots\!21\)\( T^{12} )^{2} \))
$89$ (\( ( 1 - 7921 T )( 1 + 7921 T ) \))(\( 1 - 474457834 T^{2} + 111655192487117862 T^{4} - \)\(17\!\cdots\!66\)\( T^{6} + \)\(19\!\cdots\!11\)\( T^{8} - \)\(17\!\cdots\!92\)\( T^{10} + \)\(12\!\cdots\!28\)\( T^{12} - \)\(68\!\cdots\!52\)\( T^{14} + \)\(30\!\cdots\!71\)\( T^{16} - \)\(10\!\cdots\!06\)\( T^{18} + \)\(26\!\cdots\!02\)\( T^{20} - \)\(44\!\cdots\!34\)\( T^{22} + \)\(37\!\cdots\!81\)\( T^{24} \))
$97$ (\( 1 - 18431 T + 88529281 T^{2} \))(\( ( 1 + 2921 T + 384124299 T^{2} + 837647682043 T^{3} + 69794294829141482 T^{4} + \)\(11\!\cdots\!33\)\( T^{5} + \)\(76\!\cdots\!95\)\( T^{6} + \)\(10\!\cdots\!73\)\( T^{7} + \)\(54\!\cdots\!02\)\( T^{8} + \)\(58\!\cdots\!63\)\( T^{9} + \)\(23\!\cdots\!79\)\( T^{10} + \)\(15\!\cdots\!21\)\( T^{11} + \)\(48\!\cdots\!81\)\( T^{12} )^{2} \))
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