# Properties

 Label 11.4.c Level 11 Weight 4 Character orbit c Rep. character $$\chi_{11}(3,\cdot)$$ Character field $$\Q(\zeta_{5})$$ Dimension 8 Newform subspaces 1 Sturm bound 4 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 11.c (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$1$$ Sturm bound: $$4$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(11, [\chi])$$.

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

## Trace form

 $$8q - 7q^{2} - 3q^{3} + 3q^{4} - 7q^{5} - 29q^{6} - 35q^{7} + 47q^{8} + 31q^{9} + O(q^{10})$$ $$8q - 7q^{2} - 3q^{3} + 3q^{4} - 7q^{5} - 29q^{6} - 35q^{7} + 47q^{8} + 31q^{9} + 40q^{10} + 67q^{11} + 190q^{12} - 65q^{13} - 196q^{14} - 121q^{15} - 377q^{16} - 31q^{17} - 102q^{18} + 148q^{19} + 342q^{20} + 334q^{21} + 647q^{22} - 12q^{23} - 447q^{24} - 201q^{25} - 140q^{26} + 72q^{27} - 42q^{28} - 199q^{29} - 114q^{30} - 361q^{31} + 324q^{32} - 232q^{33} - 298q^{34} + 237q^{35} + 120q^{36} + 81q^{37} - 52q^{38} + 365q^{39} + 532q^{40} - 31q^{41} + 170q^{42} - 650q^{43} - 1208q^{44} + 452q^{45} + 1204q^{46} + 857q^{47} + 644q^{48} + 1375q^{49} - 147q^{50} - 246q^{51} - 590q^{52} - 1493q^{53} - 3100q^{54} - 1583q^{55} - 1560q^{56} + 102q^{57} + 1392q^{58} + 676q^{59} + 1068q^{60} - 525q^{61} + 2456q^{62} - 68q^{63} + 471q^{64} + 1790q^{65} + 1014q^{66} + 86q^{67} + 710q^{68} - 42q^{69} - 144q^{70} + 1143q^{71} + 919q^{72} - 2155q^{73} - 1476q^{74} - 160q^{75} - 242q^{76} - 2015q^{77} - 1340q^{78} - 861q^{79} - 1916q^{80} - 26q^{81} - 3497q^{82} + 52q^{83} - 84q^{84} + 2383q^{85} + 1061q^{86} + 2310q^{87} + 4543q^{88} + 3782q^{89} - 1682q^{90} + 135q^{91} - 2450q^{92} - 2077q^{93} + 702q^{94} - 1317q^{95} + 1252q^{96} - 1344q^{97} + 2740q^{98} + 2099q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(11, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
11.4.c.a $$8$$ $$0.649$$ 8.0.$$\cdots$$.1 None $$-7$$ $$-3$$ $$-7$$ $$-35$$ $$q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 7 T + 15 T^{2} - 17 T^{3} - 81 T^{4} + 366 T^{5} + 1624 T^{6} - 1744 T^{7} - 17904 T^{8} - 13952 T^{9} + 103936 T^{10} + 187392 T^{11} - 331776 T^{12} - 557056 T^{13} + 3932160 T^{14} + 14680064 T^{15} + 16777216 T^{16}$$
$3$ $$1 + 3 T - 38 T^{2} - 174 T^{3} + 778 T^{4} + 4539 T^{5} - 9341 T^{6} - 51492 T^{7} + 85048 T^{8} - 1390284 T^{9} - 6809589 T^{10} + 89341137 T^{11} + 413461098 T^{12} - 2496709818 T^{13} - 14721978582 T^{14} + 31381059609 T^{15} + 282429536481 T^{16}$$
$5$ $$1 + 7 T - 518 T^{3} - 1266 T^{4} - 256767 T^{5} - 39725 T^{6} + 1239098 T^{7} + 146654796 T^{8} + 154887250 T^{9} - 620703125 T^{10} - 501498046875 T^{11} - 309082031250 T^{12} - 15808105468750 T^{13} + 3337860107421875 T^{15} + 59604644775390625 T^{16}$$
$7$ $$1 + 35 T - 418 T^{2} - 32140 T^{3} - 221250 T^{4} + 13130885 T^{5} + 294623937 T^{6} - 1901444100 T^{7} - 135159872636 T^{8} - 652195326300 T^{9} + 34662211564113 T^{10} + 529878572852195 T^{11} - 3062384793221250 T^{12} - 152586626929568020 T^{13} - 680676883926567682 T^{14} + 19549105242914940245 T^{15} +$$$$19\!\cdots\!01$$$$T^{16}$$
$11$ $$1 - 67 T + 1463 T^{2} - 67639 T^{3} + 4205960 T^{4} - 90027509 T^{5} + 2591793743 T^{6} - 157982495297 T^{7} + 3138428376721 T^{8}$$
$13$ $$1 + 65 T - 3774 T^{2} - 299880 T^{3} + 2516892 T^{4} + 764350785 T^{5} + 39746687433 T^{6} - 593220674550 T^{7} - 134342539611120 T^{8} - 1303305821986350 T^{9} + 191849668621791297 T^{10} + 8105557420284557805 T^{11} + 58638764060091449052 T^{12} -$$$$15\!\cdots\!60$$$$T^{13} -$$$$42\!\cdots\!46$$$$T^{14} +$$$$16\!\cdots\!45$$$$T^{15} +$$$$54\!\cdots\!61$$$$T^{16}$$
$17$ $$1 + 31 T - 792 T^{2} - 523972 T^{3} + 3004088 T^{4} - 470896367 T^{5} + 53763531151 T^{6} - 2458004448816 T^{7} + 615070592257928 T^{8} - 12076175857033008 T^{9} + 1297720942840911919 T^{10} - 55842600212681986399 T^{11} +$$$$17\!\cdots\!68$$$$T^{12} -$$$$14\!\cdots\!96$$$$T^{13} -$$$$11\!\cdots\!28$$$$T^{14} +$$$$21\!\cdots\!27$$$$T^{15} +$$$$33\!\cdots\!21$$$$T^{16}$$
$19$ $$1 - 148 T + 11575 T^{2} - 1444790 T^{3} + 194162525 T^{4} - 16652433274 T^{5} + 1325481769157 T^{6} - 142885089670400 T^{7} + 13417456053996940 T^{8} - 980048830049273600 T^{9} + 62358457579429692317 T^{10} -$$$$53\!\cdots\!46$$$$T^{11} +$$$$42\!\cdots\!25$$$$T^{12} -$$$$21\!\cdots\!10$$$$T^{13} +$$$$12\!\cdots\!75$$$$T^{14} -$$$$10\!\cdots\!12$$$$T^{15} +$$$$48\!\cdots\!21$$$$T^{16}$$
$23$ $$( 1 + 6 T + 27488 T^{2} + 757614 T^{3} + 422704798 T^{4} + 9217889538 T^{5} + 4069210516832 T^{6} + 10806915968778 T^{7} + 21914624432020321 T^{8} )^{2}$$
$29$ $$1 + 199 T + 14972 T^{2} + 3155808 T^{3} + 811239992 T^{4} + 144591222505 T^{5} + 23423431670163 T^{6} + 4517385217828956 T^{7} + 793290858128995600 T^{8} +$$$$11\!\cdots\!84$$$$T^{9} +$$$$13\!\cdots\!23$$$$T^{10} +$$$$20\!\cdots\!45$$$$T^{11} +$$$$28\!\cdots\!72$$$$T^{12} +$$$$27\!\cdots\!92$$$$T^{13} +$$$$31\!\cdots\!92$$$$T^{14} +$$$$10\!\cdots\!71$$$$T^{15} +$$$$12\!\cdots\!81$$$$T^{16}$$
$31$ $$1 + 361 T + 68292 T^{2} + 8747944 T^{3} + 1502105536 T^{4} - 10476370985 T^{5} - 64833894853287 T^{6} - 17021745180201160 T^{7} - 2614984674824755148 T^{8} -$$$$50\!\cdots\!60$$$$T^{9} -$$$$57\!\cdots\!47$$$$T^{10} -$$$$27\!\cdots\!35$$$$T^{11} +$$$$11\!\cdots\!96$$$$T^{12} +$$$$20\!\cdots\!44$$$$T^{13} +$$$$47\!\cdots\!72$$$$T^{14} +$$$$75\!\cdots\!91$$$$T^{15} +$$$$62\!\cdots\!21$$$$T^{16}$$
$37$ $$1 - 81 T - 78732 T^{2} + 413682 T^{3} + 4985376798 T^{4} + 13237102557 T^{5} - 205379482511809 T^{6} + 1480099189059246 T^{7} + 6444772391025324588 T^{8} + 74971464223417987638 T^{9} -$$$$52\!\cdots\!81$$$$T^{10} +$$$$17\!\cdots\!89$$$$T^{11} +$$$$32\!\cdots\!38$$$$T^{12} +$$$$13\!\cdots\!26$$$$T^{13} -$$$$13\!\cdots\!28$$$$T^{14} -$$$$69\!\cdots\!97$$$$T^{15} +$$$$43\!\cdots\!61$$$$T^{16}$$
$41$ $$1 + 31 T - 41412 T^{2} + 41956 T^{3} + 4511377452 T^{4} + 946844618625 T^{5} - 140505296388233 T^{6} + 5245993854286808 T^{7} + 10132197830913446520 T^{8} +$$$$36\!\cdots\!68$$$$T^{9} -$$$$66\!\cdots\!53$$$$T^{10} +$$$$30\!\cdots\!25$$$$T^{11} +$$$$10\!\cdots\!12$$$$T^{12} +$$$$65\!\cdots\!56$$$$T^{13} -$$$$44\!\cdots\!52$$$$T^{14} +$$$$22\!\cdots\!71$$$$T^{15} +$$$$50\!\cdots\!61$$$$T^{16}$$
$43$ $$( 1 + 325 T + 241017 T^{2} + 48348645 T^{3} + 24393602404 T^{4} + 3844055718015 T^{5} + 1523555957980833 T^{6} + 163342598879473975 T^{7} + 39959630797262576401 T^{8} )^{2}$$
$47$ $$1 - 857 T + 121092 T^{2} + 122368114 T^{3} - 61023105504 T^{4} + 11078984252823 T^{5} + 420607797631015 T^{6} - 1505063442345718948 T^{7} +$$$$72\!\cdots\!64$$$$T^{8} -$$$$15\!\cdots\!04$$$$T^{9} +$$$$45\!\cdots\!35$$$$T^{10} +$$$$12\!\cdots\!41$$$$T^{11} -$$$$70\!\cdots\!64$$$$T^{12} +$$$$14\!\cdots\!02$$$$T^{13} +$$$$15\!\cdots\!88$$$$T^{14} -$$$$11\!\cdots\!79$$$$T^{15} +$$$$13\!\cdots\!81$$$$T^{16}$$
$53$ $$1 + 1493 T + 684042 T^{2} - 45129934 T^{3} - 136433012142 T^{4} - 36785759748711 T^{5} + 3910583895798949 T^{6} + 5538380615310974548 T^{7} +$$$$24\!\cdots\!28$$$$T^{8} +$$$$82\!\cdots\!96$$$$T^{9} +$$$$86\!\cdots\!21$$$$T^{10} -$$$$12\!\cdots\!63$$$$T^{11} -$$$$67\!\cdots\!22$$$$T^{12} -$$$$33\!\cdots\!38$$$$T^{13} +$$$$74\!\cdots\!38$$$$T^{14} +$$$$24\!\cdots\!29$$$$T^{15} +$$$$24\!\cdots\!81$$$$T^{16}$$
$59$ $$1 - 676 T - 75509 T^{2} + 9379530 T^{3} + 128650837633 T^{4} - 34757410557650 T^{5} - 18754376858866031 T^{6} - 1699130425604624376 T^{7} +$$$$76\!\cdots\!28$$$$T^{8} -$$$$34\!\cdots\!04$$$$T^{9} -$$$$79\!\cdots\!71$$$$T^{10} -$$$$30\!\cdots\!50$$$$T^{11} +$$$$22\!\cdots\!73$$$$T^{12} +$$$$34\!\cdots\!70$$$$T^{13} -$$$$56\!\cdots\!89$$$$T^{14} -$$$$10\!\cdots\!84$$$$T^{15} +$$$$31\!\cdots\!61$$$$T^{16}$$
$61$ $$1 + 525 T - 238754 T^{2} - 162289050 T^{3} - 31751133810 T^{4} - 278276538435 T^{5} + 17785841568589049 T^{6} + 2328023641412643300 T^{7} -$$$$43\!\cdots\!16$$$$T^{8} +$$$$52\!\cdots\!00$$$$T^{9} +$$$$91\!\cdots\!89$$$$T^{10} -$$$$32\!\cdots\!35$$$$T^{11} -$$$$84\!\cdots\!10$$$$T^{12} -$$$$97\!\cdots\!50$$$$T^{13} -$$$$32\!\cdots\!74$$$$T^{14} +$$$$16\!\cdots\!25$$$$T^{15} +$$$$70\!\cdots\!41$$$$T^{16}$$
$67$ $$( 1 - 43 T + 808331 T^{2} - 155629659 T^{3} + 296445352544 T^{4} - 46807643129817 T^{5} + 73120314517049939 T^{6} - 1169880979040682721 T^{7} +$$$$81\!\cdots\!61$$$$T^{8} )^{2}$$
$71$ $$1 - 1143 T + 717774 T^{2} - 426999060 T^{3} + 398304224128 T^{4} - 150060483633915 T^{5} - 16487601883081509 T^{6} + 18708832368626731338 T^{7} +$$$$60\!\cdots\!48$$$$T^{8} +$$$$66\!\cdots\!18$$$$T^{9} -$$$$21\!\cdots\!89$$$$T^{10} -$$$$68\!\cdots\!65$$$$T^{11} +$$$$65\!\cdots\!48$$$$T^{12} -$$$$25\!\cdots\!60$$$$T^{13} +$$$$15\!\cdots\!14$$$$T^{14} -$$$$85\!\cdots\!53$$$$T^{15} +$$$$26\!\cdots\!81$$$$T^{16}$$
$73$ $$1 + 2155 T + 2185548 T^{2} + 1809165000 T^{3} + 1562803949820 T^{4} + 1050489744927825 T^{5} + 520439165741232123 T^{6} +$$$$31\!\cdots\!60$$$$T^{7} +$$$$21\!\cdots\!64$$$$T^{8} +$$$$12\!\cdots\!20$$$$T^{9} +$$$$78\!\cdots\!47$$$$T^{10} +$$$$61\!\cdots\!25$$$$T^{11} +$$$$35\!\cdots\!20$$$$T^{12} +$$$$16\!\cdots\!00$$$$T^{13} +$$$$75\!\cdots\!12$$$$T^{14} +$$$$29\!\cdots\!15$$$$T^{15} +$$$$52\!\cdots\!41$$$$T^{16}$$
$79$ $$1 + 861 T - 428248 T^{2} - 602343768 T^{3} + 107104581192 T^{4} + 169355011342215 T^{5} - 103898581181934707 T^{6} - 30048205990965814356 T^{7} +$$$$59\!\cdots\!00$$$$T^{8} -$$$$14\!\cdots\!84$$$$T^{9} -$$$$25\!\cdots\!47$$$$T^{10} +$$$$20\!\cdots\!85$$$$T^{11} +$$$$63\!\cdots\!72$$$$T^{12} -$$$$17\!\cdots\!32$$$$T^{13} -$$$$61\!\cdots\!28$$$$T^{14} +$$$$60\!\cdots\!19$$$$T^{15} +$$$$34\!\cdots\!81$$$$T^{16}$$
$83$ $$1 - 52 T - 837901 T^{2} - 580716282 T^{3} + 33426101033 T^{4} + 830942030041778 T^{5} + 400459572181036761 T^{6} -$$$$26\!\cdots\!76$$$$T^{7} -$$$$36\!\cdots\!72$$$$T^{8} -$$$$15\!\cdots\!12$$$$T^{9} +$$$$13\!\cdots\!09$$$$T^{10} +$$$$15\!\cdots\!34$$$$T^{11} +$$$$35\!\cdots\!13$$$$T^{12} -$$$$35\!\cdots\!74$$$$T^{13} -$$$$29\!\cdots\!09$$$$T^{14} -$$$$10\!\cdots\!16$$$$T^{15} +$$$$11\!\cdots\!21$$$$T^{16}$$
$89$ $$( 1 - 1891 T + 3678143 T^{2} - 4008289261 T^{3} + 4189944324368 T^{4} - 2825719672037909 T^{5} + 1827968256479165423 T^{6} -$$$$66\!\cdots\!19$$$$T^{7} +$$$$24\!\cdots\!21$$$$T^{8} )^{2}$$
$97$ $$1 + 1344 T + 412889 T^{2} + 1296130300 T^{3} + 2215229286991 T^{4} + 1422791121306492 T^{5} + 1824021419147257715 T^{6} +$$$$23\!\cdots\!68$$$$T^{7} +$$$$18\!\cdots\!72$$$$T^{8} +$$$$21\!\cdots\!64$$$$T^{9} +$$$$15\!\cdots\!35$$$$T^{10} +$$$$10\!\cdots\!64$$$$T^{11} +$$$$15\!\cdots\!31$$$$T^{12} +$$$$82\!\cdots\!00$$$$T^{13} +$$$$23\!\cdots\!21$$$$T^{14} +$$$$70\!\cdots\!68$$$$T^{15} +$$$$48\!\cdots\!81$$$$T^{16}$$