Properties

Label 11.11
Level 11
Weight 11
Dimension 45
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 110
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(110\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(11))\).

Total New Old
Modular forms 55 55 0
Cusp forms 45 45 0
Eisenstein series 10 10 0

Trace form

\( 45q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} - 3525q^{6} - 9740q^{7} - 56325q^{8} + 198545q^{9} + O(q^{10}) \) \( 45q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} - 3525q^{6} - 9740q^{7} - 56325q^{8} + 198545q^{9} - 245200q^{11} - 317450q^{12} + 516610q^{13} + 96410q^{14} - 61495q^{15} - 179745q^{16} - 1563930q^{17} - 3716190q^{18} + 6441265q^{19} + 16211140q^{20} - 29049275q^{22} - 19203795q^{23} - 6935455q^{24} + 62455685q^{25} + 61650650q^{26} - 38545490q^{27} - 158441860q^{28} - 30773770q^{29} + 164452420q^{30} + 155856685q^{31} - 318996030q^{33} - 16160070q^{34} + 93755030q^{35} + 67473990q^{36} - 125448075q^{37} + 109342140q^{38} + 13696700q^{39} + 66388740q^{40} + 168755230q^{41} + 54207230q^{42} + 822430600q^{44} - 1232915140q^{45} - 843022850q^{46} - 592219270q^{47} - 458884920q^{48} + 758776970q^{49} + 1888812255q^{50} + 2730932925q^{51} - 1016067090q^{52} - 1495992580q^{53} + 801748135q^{55} + 526524340q^{56} - 1846600035q^{57} - 7980213620q^{58} - 2451810080q^{59} + 2412560860q^{60} + 4185015940q^{61} + 8028589520q^{62} + 5208740790q^{63} + 4907781175q^{64} - 7249567290q^{66} - 8139514625q^{67} - 12578329400q^{68} - 5687707475q^{69} - 4341760940q^{70} + 4604271975q^{71} + 14192383525q^{72} + 6815310530q^{73} + 27099775830q^{74} + 22395754365q^{75} - 20989098770q^{77} - 52369004240q^{78} - 28511789960q^{79} - 12669286300q^{80} + 4593744095q^{81} + 5066108185q^{82} + 6078874665q^{83} + 75048937530q^{84} + 52883120010q^{85} + 36398318275q^{86} - 56740848725q^{88} - 39773682245q^{89} - 98405028320q^{90} - 57076722290q^{91} - 41759733300q^{92} + 19079675445q^{93} + 94886813720q^{94} + 79444332050q^{95} + 162737230420q^{96} + 56595302880q^{97} - 76782985105q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(11))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
11.11.b \(\chi_{11}(10, \cdot)\) 11.11.b.a 1 1
11.11.b.b 8
11.11.d \(\chi_{11}(2, \cdot)\) 11.11.d.a 36 4

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 32 T )( 1 + 32 T ) \))(\( 1 - 2162 T^{2} + 4023928 T^{4} - 5589355904 T^{6} + 6016318320640 T^{8} - 5860864456392704 T^{10} + 4424355625333424128 T^{12} - \)\(24\!\cdots\!12\)\( T^{14} + \)\(12\!\cdots\!76\)\( T^{16} \))
$3$ (\( 1 - 475 T + 59049 T^{2} \))(\( ( 1 + 201 T + 137277 T^{2} + 34455618 T^{3} + 10388320470 T^{4} + 2034569787282 T^{5} + 478655302216077 T^{6} + 41384117551024449 T^{7} + 12157665459056928801 T^{8} )^{2} \))
$5$ (\( 1 + 3001 T + 9765625 T^{2} \))(\( ( 1 - 1215 T + 17750585 T^{2} - 37860921450 T^{3} + 173386121112150 T^{4} - 369735561035156250 T^{5} + \)\(16\!\cdots\!25\)\( T^{6} - \)\(11\!\cdots\!75\)\( T^{7} + \)\(90\!\cdots\!25\)\( T^{8} )^{2} \))
$7$ (\( ( 1 - 16807 T )( 1 + 16807 T ) \))(\( 1 - 1491912152 T^{2} + 1035306481549364668 T^{4} - \)\(45\!\cdots\!44\)\( T^{6} + \)\(14\!\cdots\!70\)\( T^{8} - \)\(36\!\cdots\!44\)\( T^{10} + \)\(65\!\cdots\!68\)\( T^{12} - \)\(75\!\cdots\!52\)\( T^{14} + \)\(40\!\cdots\!01\)\( T^{16} \))
$11$ (\( 1 + 161051 T \))(\( 1 - 40128 T + 56342385308 T^{2} - 1574505273523776 T^{3} + \)\(17\!\cdots\!70\)\( T^{4} - \)\(40\!\cdots\!76\)\( T^{5} + \)\(37\!\cdots\!08\)\( T^{6} - \)\(70\!\cdots\!28\)\( T^{7} + \)\(45\!\cdots\!01\)\( T^{8} \))
$13$ (\( ( 1 - 371293 T )( 1 + 371293 T ) \))(\( 1 - 421628779352 T^{2} + \)\(14\!\cdots\!68\)\( T^{4} - \)\(28\!\cdots\!24\)\( T^{6} + \)\(46\!\cdots\!90\)\( T^{8} - \)\(53\!\cdots\!24\)\( T^{10} + \)\(50\!\cdots\!68\)\( T^{12} - \)\(28\!\cdots\!52\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} \))
$17$ (\( ( 1 - 1419857 T )( 1 + 1419857 T ) \))(\( 1 - 1337737418072 T^{2} + \)\(11\!\cdots\!88\)\( T^{4} - \)\(13\!\cdots\!84\)\( T^{6} + \)\(67\!\cdots\!90\)\( T^{8} - \)\(54\!\cdots\!84\)\( T^{10} + \)\(19\!\cdots\!88\)\( T^{12} - \)\(89\!\cdots\!72\)\( T^{14} + \)\(27\!\cdots\!01\)\( T^{16} \))
$19$ (\( ( 1 - 2476099 T )( 1 + 2476099 T ) \))(\( 1 - 20453172313688 T^{2} + \)\(21\!\cdots\!48\)\( T^{4} - \)\(18\!\cdots\!76\)\( T^{6} + \)\(13\!\cdots\!10\)\( T^{8} - \)\(69\!\cdots\!76\)\( T^{10} + \)\(30\!\cdots\!48\)\( T^{12} - \)\(10\!\cdots\!88\)\( T^{14} + \)\(19\!\cdots\!01\)\( T^{16} \))
$23$ (\( 1 + 11910325 T + 41426511213649 T^{2} \))(\( ( 1 + 5142561 T + 110966713041557 T^{2} + \)\(35\!\cdots\!78\)\( T^{3} + \)\(54\!\cdots\!30\)\( T^{4} + \)\(14\!\cdots\!22\)\( T^{5} + \)\(19\!\cdots\!57\)\( T^{6} + \)\(36\!\cdots\!89\)\( T^{7} + \)\(29\!\cdots\!01\)\( T^{8} )^{2} \))
$29$ (\( ( 1 - 20511149 T )( 1 + 20511149 T ) \))(\( 1 - 2658155860573448 T^{2} + \)\(32\!\cdots\!28\)\( T^{4} - \)\(24\!\cdots\!16\)\( T^{6} + \)\(12\!\cdots\!50\)\( T^{8} - \)\(43\!\cdots\!16\)\( T^{10} + \)\(10\!\cdots\!28\)\( T^{12} - \)\(14\!\cdots\!48\)\( T^{14} + \)\(98\!\cdots\!01\)\( T^{16} \))
$31$ (\( 1 - 3192323 T + 819628286980801 T^{2} \))(\( ( 1 - 44582183 T + 2832177215899813 T^{2} - \)\(79\!\cdots\!46\)\( T^{3} + \)\(31\!\cdots\!10\)\( T^{4} - \)\(65\!\cdots\!46\)\( T^{5} + \)\(19\!\cdots\!13\)\( T^{6} - \)\(24\!\cdots\!83\)\( T^{7} + \)\(45\!\cdots\!01\)\( T^{8} )^{2} \))
$37$ (\( 1 + 137082625 T + 4808584372417849 T^{2} \))(\( ( 1 - 15824951 T + 10196625472058617 T^{2} - \)\(11\!\cdots\!38\)\( T^{3} + \)\(69\!\cdots\!30\)\( T^{4} - \)\(53\!\cdots\!62\)\( T^{5} + \)\(23\!\cdots\!17\)\( T^{6} - \)\(17\!\cdots\!99\)\( T^{7} + \)\(53\!\cdots\!01\)\( T^{8} )^{2} \))
$41$ (\( ( 1 - 115856201 T )( 1 + 115856201 T ) \))(\( 1 - 33642537742470488 T^{2} + \)\(85\!\cdots\!08\)\( T^{4} - \)\(14\!\cdots\!36\)\( T^{6} + \)\(23\!\cdots\!10\)\( T^{8} - \)\(26\!\cdots\!36\)\( T^{10} + \)\(27\!\cdots\!08\)\( T^{12} - \)\(19\!\cdots\!88\)\( T^{14} + \)\(10\!\cdots\!01\)\( T^{16} \))
$43$ (\( ( 1 - 147008443 T )( 1 + 147008443 T ) \))(\( 1 - 50337771744886472 T^{2} + \)\(17\!\cdots\!48\)\( T^{4} - \)\(39\!\cdots\!44\)\( T^{6} + \)\(90\!\cdots\!70\)\( T^{8} - \)\(18\!\cdots\!44\)\( T^{10} + \)\(38\!\cdots\!48\)\( T^{12} - \)\(51\!\cdots\!72\)\( T^{14} + \)\(47\!\cdots\!01\)\( T^{16} \))
$47$ (\( 1 - 151795250 T + 52599132235830049 T^{2} \))(\( ( 1 + 371274144 T + 179516078138049212 T^{2} + \)\(57\!\cdots\!92\)\( T^{3} + \)\(13\!\cdots\!30\)\( T^{4} + \)\(30\!\cdots\!08\)\( T^{5} + \)\(49\!\cdots\!12\)\( T^{6} + \)\(54\!\cdots\!56\)\( T^{7} + \)\(76\!\cdots\!01\)\( T^{8} )^{2} \))
$53$ (\( 1 - 375066650 T + 174887470365513049 T^{2} \))(\( ( 1 + 148312296 T + 428377223611984412 T^{2} + \)\(81\!\cdots\!88\)\( T^{3} + \)\(92\!\cdots\!90\)\( T^{4} + \)\(14\!\cdots\!12\)\( T^{5} + \)\(13\!\cdots\!12\)\( T^{6} + \)\(79\!\cdots\!04\)\( T^{7} + \)\(93\!\cdots\!01\)\( T^{8} )^{2} \))
$59$ (\( 1 + 813567973 T + 511116753300641401 T^{2} \))(\( ( 1 - 734972247 T + 1393141461361633613 T^{2} - \)\(85\!\cdots\!34\)\( T^{3} + \)\(88\!\cdots\!10\)\( T^{4} - \)\(43\!\cdots\!34\)\( T^{5} + \)\(36\!\cdots\!13\)\( T^{6} - \)\(98\!\cdots\!47\)\( T^{7} + \)\(68\!\cdots\!01\)\( T^{8} )^{2} \))
$61$ (\( ( 1 - 844596301 T )( 1 + 844596301 T ) \))(\( 1 - 3625010353661962568 T^{2} + \)\(67\!\cdots\!68\)\( T^{4} - \)\(80\!\cdots\!96\)\( T^{6} + \)\(67\!\cdots\!70\)\( T^{8} - \)\(40\!\cdots\!96\)\( T^{10} + \)\(17\!\cdots\!68\)\( T^{12} - \)\(47\!\cdots\!68\)\( T^{14} + \)\(67\!\cdots\!01\)\( T^{16} \))
$67$ (\( 1 - 2616638675 T + 1822837804551761449 T^{2} \))(\( ( 1 + 2041193089 T + 8397320418930605917 T^{2} + \)\(11\!\cdots\!62\)\( T^{3} + \)\(23\!\cdots\!10\)\( T^{4} + \)\(20\!\cdots\!38\)\( T^{5} + \)\(27\!\cdots\!17\)\( T^{6} + \)\(12\!\cdots\!61\)\( T^{7} + \)\(11\!\cdots\!01\)\( T^{8} )^{2} \))
$71$ (\( 1 - 783651827 T + 3255243551009881201 T^{2} \))(\( ( 1 + 855799017 T + 6730553772766894613 T^{2} + \)\(10\!\cdots\!74\)\( T^{3} + \)\(23\!\cdots\!70\)\( T^{4} + \)\(34\!\cdots\!74\)\( T^{5} + \)\(71\!\cdots\!13\)\( T^{6} + \)\(29\!\cdots\!17\)\( T^{7} + \)\(11\!\cdots\!01\)\( T^{8} )^{2} \))
$73$ (\( ( 1 - 2073071593 T )( 1 + 2073071593 T ) \))(\( 1 - 20358512827675404632 T^{2} + \)\(20\!\cdots\!88\)\( T^{4} - \)\(13\!\cdots\!64\)\( T^{6} + \)\(64\!\cdots\!10\)\( T^{8} - \)\(24\!\cdots\!64\)\( T^{10} + \)\(69\!\cdots\!88\)\( T^{12} - \)\(12\!\cdots\!32\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} \))
$79$ (\( ( 1 - 3077056399 T )( 1 + 3077056399 T ) \))(\( 1 - 39359924975996928008 T^{2} + \)\(74\!\cdots\!68\)\( T^{4} - \)\(10\!\cdots\!96\)\( T^{6} + \)\(10\!\cdots\!50\)\( T^{8} - \)\(91\!\cdots\!96\)\( T^{10} + \)\(60\!\cdots\!68\)\( T^{12} - \)\(28\!\cdots\!08\)\( T^{14} + \)\(64\!\cdots\!01\)\( T^{16} \))
$83$ (\( ( 1 - 3939040643 T )( 1 + 3939040643 T ) \))(\( 1 - 66182368698510495752 T^{2} + \)\(23\!\cdots\!88\)\( T^{4} - \)\(57\!\cdots\!84\)\( T^{6} + \)\(10\!\cdots\!30\)\( T^{8} - \)\(13\!\cdots\!84\)\( T^{10} + \)\(13\!\cdots\!88\)\( T^{12} - \)\(92\!\cdots\!52\)\( T^{14} + \)\(33\!\cdots\!01\)\( T^{16} \))
$89$ (\( 1 + 2870912977 T + 31181719929966183601 T^{2} \))(\( ( 1 + 8860741473 T + \)\(12\!\cdots\!53\)\( T^{2} + \)\(80\!\cdots\!66\)\( T^{3} + \)\(60\!\cdots\!50\)\( T^{4} + \)\(24\!\cdots\!66\)\( T^{5} + \)\(12\!\cdots\!53\)\( T^{6} + \)\(26\!\cdots\!73\)\( T^{7} + \)\(94\!\cdots\!01\)\( T^{8} )^{2} \))
$97$ (\( 1 - 9454010975 T + 73742412689492826049 T^{2} \))(\( ( 1 - 27503734991 T + \)\(41\!\cdots\!57\)\( T^{2} - \)\(42\!\cdots\!18\)\( T^{3} + \)\(38\!\cdots\!70\)\( T^{4} - \)\(31\!\cdots\!82\)\( T^{5} + \)\(22\!\cdots\!57\)\( T^{6} - \)\(11\!\cdots\!59\)\( T^{7} + \)\(29\!\cdots\!01\)\( T^{8} )^{2} \))
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