Properties

Label 11.10.a
Level 11
Weight 10
Character orbit a
Rep. character \(\chi_{11}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 2
Sturm bound 10
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(11))\).

Total New Old
Modular forms 10 8 2
Cusp forms 8 8 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(11\)Dim.
\(+\)\(3\)
\(-\)\(5\)

Trace form

\( 8q + 16q^{2} - 74q^{3} + 1620q^{4} - 230q^{5} - 578q^{6} + 1140q^{7} + 20652q^{8} + 89342q^{9} + O(q^{10}) \) \( 8q + 16q^{2} - 74q^{3} + 1620q^{4} - 230q^{5} - 578q^{6} + 1140q^{7} + 20652q^{8} + 89342q^{9} - 83738q^{10} + 29282q^{11} + 39248q^{12} - 46044q^{13} + 24412q^{14} - 19106q^{15} - 432120q^{16} - 528560q^{17} + 1174610q^{18} - 1190296q^{19} - 2069896q^{20} - 462428q^{21} + 234256q^{22} + 5090582q^{23} + 488700q^{24} + 4604214q^{25} + 3194668q^{26} - 5045294q^{27} - 5047520q^{28} + 3174756q^{29} + 4505830q^{30} + 7205094q^{31} - 18294040q^{32} + 4363018q^{33} - 5679944q^{34} - 14501708q^{35} - 5775164q^{36} - 1798954q^{37} + 1039992q^{38} + 54037792q^{39} - 27552684q^{40} - 4175684q^{41} - 73685276q^{42} + 47957684q^{43} - 2986764q^{44} - 23906560q^{45} - 21202042q^{46} + 2547848q^{47} + 173389640q^{48} + 52376928q^{49} + 188003306q^{50} - 197964644q^{51} + 98761240q^{52} - 41405544q^{53} - 248932046q^{54} + 50042938q^{55} + 35350008q^{56} - 300438024q^{57} - 57004092q^{58} + 345886082q^{59} + 81928544q^{60} + 225292700q^{61} - 248605562q^{62} - 117057784q^{63} - 467302720q^{64} - 496809896q^{65} + 312351094q^{66} + 653677834q^{67} - 1061562904q^{68} - 165010498q^{69} + 1585529068q^{70} - 48179694q^{71} + 1470546336q^{72} - 299529612q^{73} - 452221206q^{74} - 1525780696q^{75} - 841669744q^{76} + 229278060q^{77} + 2174191720q^{78} - 1467250820q^{79} + 17771864q^{80} + 3123036200q^{81} + 289855036q^{82} + 1618138740q^{83} - 3190963840q^{84} + 827755396q^{85} - 1505983188q^{86} - 2316789168q^{87} + 889879980q^{88} + 152250798q^{89} - 7038414304q^{90} - 1260663328q^{91} + 5457058144q^{92} + 1764718990q^{93} + 5948451440q^{94} - 2704939944q^{95} + 1363238456q^{96} - 2447938502q^{97} - 3560544360q^{98} + 881915276q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(11))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
11.10.a.a \(3\) \(5.665\) 3.3.2659452.1 None \(0\) \(-186\) \(-1824\) \(-7260\) \(+\) \(q-\beta _{1}q^{2}+(-62+4\beta _{1}-\beta _{2})q^{3}+(304+\cdots)q^{4}+\cdots\)
11.10.a.b \(5\) \(5.665\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(16\) \(112\) \(1594\) \(8400\) \(-\) \(q+(3+\beta _{1})q^{2}+(22+3\beta _{1}+\beta _{4})q^{3}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 312 T^{2} + 6688 T^{3} + 159744 T^{4} + 134217728 T^{6} \))(\( 1 - 16 T + 1054 T^{2} - 26340 T^{3} + 927776 T^{4} - 14336320 T^{5} + 475021312 T^{6} - 6904872960 T^{7} + 141465485312 T^{8} - 1099511627776 T^{9} + 35184372088832 T^{10} \))
$3$ (\( 1 + 186 T + 39546 T^{2} + 7418736 T^{3} + 778383918 T^{4} + 72060210954 T^{5} + 7625597484987 T^{6} \))(\( 1 - 112 T + 18085 T^{2} - 2569092 T^{3} + 237153681 T^{4} - 7479450684 T^{5} + 4667895903123 T^{6} - 995318878925988 T^{7} + 137908930515989895 T^{8} - 16810599153263901552 T^{9} + \)\(29\!\cdots\!43\)\( T^{10} \))
$5$ (\( 1 + 1824 T + 5373540 T^{2} + 6504482650 T^{3} + 10495195312500 T^{4} + 6958007812500000 T^{5} + 7450580596923828125 T^{6} \))(\( 1 - 1594 T + 3070759 T^{2} - 4299329856 T^{3} + 10831557328565 T^{4} - 13283713306841650 T^{5} + 21155385407353515625 T^{6} - \)\(16\!\cdots\!00\)\( T^{7} + \)\(22\!\cdots\!75\)\( T^{8} - \)\(23\!\cdots\!50\)\( T^{9} + \)\(28\!\cdots\!25\)\( T^{10} \))
$7$ (\( 1 + 7260 T + 113999049 T^{2} + 510907138280 T^{3} + 4600272821719743 T^{4} + 11822282720829859740 T^{5} + \)\(65\!\cdots\!43\)\( T^{6} \))(\( 1 - 8400 T + 82860715 T^{2} - 559338771040 T^{3} + 5216016853662370 T^{4} - 37137975836257104928 T^{5} + \)\(21\!\cdots\!90\)\( T^{6} - \)\(91\!\cdots\!60\)\( T^{7} + \)\(54\!\cdots\!45\)\( T^{8} - \)\(22\!\cdots\!00\)\( T^{9} + \)\(10\!\cdots\!07\)\( T^{10} \))
$11$ (\( ( 1 + 14641 T )^{3} \))(\( ( 1 - 14641 T )^{5} \))
$13$ (\( 1 + 93258 T + 30322110999 T^{2} + 1904820864405668 T^{3} + \)\(32\!\cdots\!27\)\( T^{4} + \)\(10\!\cdots\!82\)\( T^{5} + \)\(11\!\cdots\!17\)\( T^{6} \))(\( 1 - 47214 T + 33002578705 T^{2} - 2711633152138744 T^{3} + \)\(51\!\cdots\!02\)\( T^{4} - \)\(45\!\cdots\!24\)\( T^{5} + \)\(54\!\cdots\!46\)\( T^{6} - \)\(30\!\cdots\!76\)\( T^{7} + \)\(39\!\cdots\!85\)\( T^{8} - \)\(59\!\cdots\!74\)\( T^{9} + \)\(13\!\cdots\!93\)\( T^{10} \))
$17$ (\( 1 - 18678 T + 244701251151 T^{2} + 8819608834790380 T^{3} + \)\(29\!\cdots\!47\)\( T^{4} - \)\(26\!\cdots\!02\)\( T^{5} + \)\(16\!\cdots\!73\)\( T^{6} \))(\( 1 + 547238 T + 503386795117 T^{2} + 187338049111023144 T^{3} + \)\(10\!\cdots\!94\)\( T^{4} + \)\(29\!\cdots\!16\)\( T^{5} + \)\(12\!\cdots\!18\)\( T^{6} + \)\(26\!\cdots\!96\)\( T^{7} + \)\(83\!\cdots\!41\)\( T^{8} + \)\(10\!\cdots\!78\)\( T^{9} + \)\(23\!\cdots\!57\)\( T^{10} \))
$19$ (\( 1 + 1027356 T + 804683662041 T^{2} + 453396340489692072 T^{3} + \)\(25\!\cdots\!39\)\( T^{4} + \)\(10\!\cdots\!96\)\( T^{5} + \)\(33\!\cdots\!39\)\( T^{6} \))(\( 1 + 162940 T + 626247383375 T^{2} + 204591429125956240 T^{3} + \)\(22\!\cdots\!70\)\( T^{4} + \)\(78\!\cdots\!40\)\( T^{5} + \)\(72\!\cdots\!30\)\( T^{6} + \)\(21\!\cdots\!40\)\( T^{7} + \)\(21\!\cdots\!25\)\( T^{8} + \)\(17\!\cdots\!40\)\( T^{9} + \)\(34\!\cdots\!99\)\( T^{10} \))
$23$ (\( 1 - 1674690 T + 1732722881190 T^{2} - 1602963245003190508 T^{3} + \)\(31\!\cdots\!70\)\( T^{4} - \)\(54\!\cdots\!10\)\( T^{5} + \)\(58\!\cdots\!47\)\( T^{6} \))(\( 1 - 3415892 T + 12451429808905 T^{2} - 24971305008143392572 T^{3} + \)\(50\!\cdots\!81\)\( T^{4} - \)\(67\!\cdots\!24\)\( T^{5} + \)\(90\!\cdots\!03\)\( T^{6} - \)\(81\!\cdots\!68\)\( T^{7} + \)\(72\!\cdots\!35\)\( T^{8} - \)\(35\!\cdots\!12\)\( T^{9} + \)\(18\!\cdots\!43\)\( T^{10} \))
$29$ (\( 1 + 2693658 T + 41416876883799 T^{2} + 72041597671730302308 T^{3} + \)\(60\!\cdots\!31\)\( T^{4} + \)\(56\!\cdots\!38\)\( T^{5} + \)\(30\!\cdots\!09\)\( T^{6} \))(\( 1 - 5868414 T + 48094980811057 T^{2} - \)\(10\!\cdots\!64\)\( T^{3} + \)\(51\!\cdots\!54\)\( T^{4} - \)\(16\!\cdots\!24\)\( T^{5} + \)\(75\!\cdots\!26\)\( T^{6} - \)\(21\!\cdots\!04\)\( T^{7} + \)\(14\!\cdots\!13\)\( T^{8} - \)\(25\!\cdots\!94\)\( T^{9} + \)\(64\!\cdots\!49\)\( T^{10} \))
$31$ (\( 1 + 4525302 T + 84482606455422 T^{2} + \)\(23\!\cdots\!20\)\( T^{3} + \)\(22\!\cdots\!62\)\( T^{4} + \)\(31\!\cdots\!82\)\( T^{5} + \)\(18\!\cdots\!11\)\( T^{6} \))(\( 1 - 11730396 T + 96705874660177 T^{2} - \)\(32\!\cdots\!32\)\( T^{3} + \)\(64\!\cdots\!21\)\( T^{4} + \)\(25\!\cdots\!28\)\( T^{5} + \)\(17\!\cdots\!91\)\( T^{6} - \)\(22\!\cdots\!12\)\( T^{7} + \)\(17\!\cdots\!47\)\( T^{8} - \)\(57\!\cdots\!76\)\( T^{9} + \)\(12\!\cdots\!51\)\( T^{10} \))
$37$ (\( 1 + 8820204 T + 323581468812468 T^{2} + \)\(23\!\cdots\!42\)\( T^{3} + \)\(42\!\cdots\!36\)\( T^{4} + \)\(14\!\cdots\!16\)\( T^{5} + \)\(21\!\cdots\!33\)\( T^{6} \))(\( 1 - 7021250 T + 430052444433383 T^{2} - \)\(30\!\cdots\!12\)\( T^{3} + \)\(93\!\cdots\!09\)\( T^{4} - \)\(54\!\cdots\!22\)\( T^{5} + \)\(12\!\cdots\!93\)\( T^{6} - \)\(51\!\cdots\!48\)\( T^{7} + \)\(94\!\cdots\!39\)\( T^{8} - \)\(20\!\cdots\!50\)\( T^{9} + \)\(37\!\cdots\!57\)\( T^{10} \))
$41$ (\( 1 + 9771102 T + 983873066035371 T^{2} + \)\(63\!\cdots\!32\)\( T^{3} + \)\(32\!\cdots\!31\)\( T^{4} + \)\(10\!\cdots\!42\)\( T^{5} + \)\(35\!\cdots\!81\)\( T^{6} \))(\( 1 - 5595418 T + 915408596557885 T^{2} - \)\(41\!\cdots\!60\)\( T^{3} + \)\(36\!\cdots\!58\)\( T^{4} + \)\(92\!\cdots\!08\)\( T^{5} + \)\(12\!\cdots\!38\)\( T^{6} - \)\(44\!\cdots\!60\)\( T^{7} + \)\(32\!\cdots\!85\)\( T^{8} - \)\(64\!\cdots\!38\)\( T^{9} + \)\(37\!\cdots\!01\)\( T^{10} \))
$43$ (\( 1 - 18795744 T + 450693902233077 T^{2} - \)\(63\!\cdots\!96\)\( T^{3} + \)\(22\!\cdots\!11\)\( T^{4} - \)\(47\!\cdots\!56\)\( T^{5} + \)\(12\!\cdots\!07\)\( T^{6} \))(\( 1 - 29161940 T + 1487036295886895 T^{2} - \)\(43\!\cdots\!40\)\( T^{3} + \)\(13\!\cdots\!10\)\( T^{4} - \)\(27\!\cdots\!64\)\( T^{5} + \)\(66\!\cdots\!30\)\( T^{6} - \)\(11\!\cdots\!60\)\( T^{7} + \)\(18\!\cdots\!65\)\( T^{8} - \)\(18\!\cdots\!40\)\( T^{9} + \)\(32\!\cdots\!43\)\( T^{10} \))
$47$ (\( 1 + 31155816 T + 1405866049149453 T^{2} + \)\(72\!\cdots\!92\)\( T^{3} + \)\(15\!\cdots\!51\)\( T^{4} + \)\(39\!\cdots\!24\)\( T^{5} + \)\(14\!\cdots\!63\)\( T^{6} \))(\( 1 - 33703664 T + 4000667127883819 T^{2} - \)\(83\!\cdots\!72\)\( T^{3} + \)\(66\!\cdots\!78\)\( T^{4} - \)\(10\!\cdots\!40\)\( T^{5} + \)\(73\!\cdots\!26\)\( T^{6} - \)\(10\!\cdots\!08\)\( T^{7} + \)\(56\!\cdots\!97\)\( T^{8} - \)\(52\!\cdots\!44\)\( T^{9} + \)\(17\!\cdots\!07\)\( T^{10} \))
$53$ (\( 1 - 47500122 T + 7107864087122523 T^{2} - \)\(31\!\cdots\!28\)\( T^{3} + \)\(23\!\cdots\!59\)\( T^{4} - \)\(51\!\cdots\!58\)\( T^{5} + \)\(35\!\cdots\!37\)\( T^{6} \))(\( 1 + 88905666 T + 14171543057009521 T^{2} + \)\(89\!\cdots\!04\)\( T^{3} + \)\(84\!\cdots\!74\)\( T^{4} + \)\(40\!\cdots\!80\)\( T^{5} + \)\(28\!\cdots\!42\)\( T^{6} + \)\(97\!\cdots\!56\)\( T^{7} + \)\(50\!\cdots\!77\)\( T^{8} + \)\(10\!\cdots\!86\)\( T^{9} + \)\(39\!\cdots\!93\)\( T^{10} \))
$59$ (\( 1 - 332138370 T + 61049524588296858 T^{2} - \)\(68\!\cdots\!48\)\( T^{3} + \)\(52\!\cdots\!62\)\( T^{4} - \)\(24\!\cdots\!70\)\( T^{5} + \)\(65\!\cdots\!19\)\( T^{6} \))(\( 1 - 13747712 T + 36554402959360429 T^{2} - \)\(58\!\cdots\!32\)\( T^{3} + \)\(57\!\cdots\!33\)\( T^{4} - \)\(80\!\cdots\!92\)\( T^{5} + \)\(50\!\cdots\!87\)\( T^{6} - \)\(44\!\cdots\!72\)\( T^{7} + \)\(23\!\cdots\!51\)\( T^{8} - \)\(77\!\cdots\!92\)\( T^{9} + \)\(48\!\cdots\!99\)\( T^{10} \))
$61$ (\( 1 + 49031730 T + 18462092029011735 T^{2} + \)\(14\!\cdots\!60\)\( T^{3} + \)\(21\!\cdots\!35\)\( T^{4} + \)\(67\!\cdots\!30\)\( T^{5} + \)\(15\!\cdots\!21\)\( T^{6} \))(\( 1 - 274324430 T + 73481705981906897 T^{2} - \)\(11\!\cdots\!52\)\( T^{3} + \)\(17\!\cdots\!30\)\( T^{4} - \)\(19\!\cdots\!72\)\( T^{5} + \)\(20\!\cdots\!30\)\( T^{6} - \)\(15\!\cdots\!12\)\( T^{7} + \)\(11\!\cdots\!37\)\( T^{8} - \)\(51\!\cdots\!30\)\( T^{9} + \)\(21\!\cdots\!01\)\( T^{10} \))
$67$ (\( 1 - 330560082 T + 88550337598210074 T^{2} - \)\(17\!\cdots\!92\)\( T^{3} + \)\(24\!\cdots\!78\)\( T^{4} - \)\(24\!\cdots\!38\)\( T^{5} + \)\(20\!\cdots\!23\)\( T^{6} \))(\( 1 - 323117752 T + 156450071982927333 T^{2} - \)\(34\!\cdots\!20\)\( T^{3} + \)\(90\!\cdots\!37\)\( T^{4} - \)\(13\!\cdots\!12\)\( T^{5} + \)\(24\!\cdots\!39\)\( T^{6} - \)\(25\!\cdots\!80\)\( T^{7} + \)\(31\!\cdots\!59\)\( T^{8} - \)\(17\!\cdots\!12\)\( T^{9} + \)\(14\!\cdots\!07\)\( T^{10} \))
$71$ (\( 1 + 57835050 T + 107442044673230142 T^{2} + \)\(28\!\cdots\!16\)\( T^{3} + \)\(49\!\cdots\!02\)\( T^{4} + \)\(12\!\cdots\!50\)\( T^{5} + \)\(96\!\cdots\!91\)\( T^{6} \))(\( 1 - 9655356 T + 159011875865452969 T^{2} - \)\(76\!\cdots\!04\)\( T^{3} + \)\(12\!\cdots\!21\)\( T^{4} - \)\(53\!\cdots\!92\)\( T^{5} + \)\(57\!\cdots\!51\)\( T^{6} - \)\(16\!\cdots\!44\)\( T^{7} + \)\(15\!\cdots\!79\)\( T^{8} - \)\(42\!\cdots\!76\)\( T^{9} + \)\(20\!\cdots\!51\)\( T^{10} \))
$73$ (\( 1 + 458816886 T + 179043981976468971 T^{2} + \)\(47\!\cdots\!28\)\( T^{3} + \)\(10\!\cdots\!23\)\( T^{4} + \)\(15\!\cdots\!34\)\( T^{5} + \)\(20\!\cdots\!97\)\( T^{6} \))(\( 1 - 159287274 T + 224789656548641245 T^{2} - \)\(37\!\cdots\!84\)\( T^{3} + \)\(22\!\cdots\!02\)\( T^{4} - \)\(32\!\cdots\!64\)\( T^{5} + \)\(13\!\cdots\!26\)\( T^{6} - \)\(12\!\cdots\!96\)\( T^{7} + \)\(45\!\cdots\!65\)\( T^{8} - \)\(19\!\cdots\!14\)\( T^{9} + \)\(70\!\cdots\!93\)\( T^{10} \))
$79$ (\( 1 + 798908748 T + 300689647984312305 T^{2} + \)\(84\!\cdots\!76\)\( T^{3} + \)\(36\!\cdots\!95\)\( T^{4} + \)\(11\!\cdots\!28\)\( T^{5} + \)\(17\!\cdots\!59\)\( T^{6} \))(\( 1 + 668342072 T + 602545492746482211 T^{2} + \)\(24\!\cdots\!12\)\( T^{3} + \)\(12\!\cdots\!42\)\( T^{4} + \)\(37\!\cdots\!72\)\( T^{5} + \)\(15\!\cdots\!98\)\( T^{6} + \)\(34\!\cdots\!32\)\( T^{7} + \)\(10\!\cdots\!49\)\( T^{8} + \)\(13\!\cdots\!12\)\( T^{9} + \)\(24\!\cdots\!99\)\( T^{10} \))
$83$ (\( 1 - 1239784920 T + 1022523328258118637 T^{2} - \)\(51\!\cdots\!04\)\( T^{3} + \)\(19\!\cdots\!11\)\( T^{4} - \)\(43\!\cdots\!80\)\( T^{5} + \)\(65\!\cdots\!27\)\( T^{6} \))(\( 1 - 378353820 T + 563017067921375095 T^{2} - \)\(16\!\cdots\!20\)\( T^{3} + \)\(13\!\cdots\!50\)\( T^{4} - \)\(34\!\cdots\!64\)\( T^{5} + \)\(25\!\cdots\!50\)\( T^{6} - \)\(57\!\cdots\!80\)\( T^{7} + \)\(36\!\cdots\!65\)\( T^{8} - \)\(46\!\cdots\!20\)\( T^{9} + \)\(22\!\cdots\!43\)\( T^{10} \))
$89$ (\( 1 + 699523368 T + 428234191146895896 T^{2} + \)\(90\!\cdots\!94\)\( T^{3} + \)\(15\!\cdots\!64\)\( T^{4} + \)\(85\!\cdots\!08\)\( T^{5} + \)\(43\!\cdots\!29\)\( T^{6} \))(\( 1 - 851774166 T + 1247132660765186971 T^{2} - \)\(94\!\cdots\!36\)\( T^{3} + \)\(82\!\cdots\!37\)\( T^{4} - \)\(44\!\cdots\!06\)\( T^{5} + \)\(28\!\cdots\!33\)\( T^{6} - \)\(11\!\cdots\!16\)\( T^{7} + \)\(53\!\cdots\!59\)\( T^{8} - \)\(12\!\cdots\!26\)\( T^{9} + \)\(52\!\cdots\!49\)\( T^{10} \))
$97$ (\( 1 + 2207436012 T + 3730952641114327320 T^{2} + \)\(35\!\cdots\!58\)\( T^{3} + \)\(28\!\cdots\!40\)\( T^{4} + \)\(12\!\cdots\!68\)\( T^{5} + \)\(43\!\cdots\!13\)\( T^{6} \))(\( 1 + 240502490 T + 1404784353800658483 T^{2} + \)\(13\!\cdots\!88\)\( T^{3} + \)\(12\!\cdots\!49\)\( T^{4} + \)\(14\!\cdots\!98\)\( T^{5} + \)\(91\!\cdots\!33\)\( T^{6} + \)\(75\!\cdots\!32\)\( T^{7} + \)\(61\!\cdots\!79\)\( T^{8} + \)\(80\!\cdots\!90\)\( T^{9} + \)\(25\!\cdots\!57\)\( T^{10} \))
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