# Properties

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

## 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

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