Properties

Label 11.6.a
Level 11
Weight 6
Character orbit a
Rep. character \(\chi_{11}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(11))\).

Total New Old
Modular forms 6 4 2
Cusp forms 4 4 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.
\(+\)\(1\)
\(-\)\(3\)

Trace form

\( 4q - 4q^{2} + 19q^{3} + 68q^{4} + 5q^{5} - 146q^{6} + 94q^{7} - 372q^{8} - 25q^{9} + O(q^{10}) \) \( 4q - 4q^{2} + 19q^{3} + 68q^{4} + 5q^{5} - 146q^{6} + 94q^{7} - 372q^{8} - 25q^{9} - 338q^{10} + 242q^{11} + 1232q^{12} - 662q^{13} - 1060q^{14} + 1939q^{15} + 1736q^{16} + 1772q^{17} - 3634q^{18} + 996q^{19} - 3176q^{20} - 1058q^{21} + 484q^{22} + 643q^{23} - 14628q^{24} - 2821q^{25} + 16724q^{26} + 925q^{27} + 23552q^{28} - 8850q^{29} + 1510q^{30} - 10541q^{31} - 17528q^{32} + 5929q^{33} + 22576q^{34} - 24418q^{35} + 5044q^{36} + 29787q^{37} - 7704q^{38} + 10660q^{39} - 18924q^{40} + 4466q^{41} - 47228q^{42} - 30234q^{43} + 12100q^{44} + 18800q^{45} - 31642q^{46} - 10064q^{47} + 64904q^{48} + 31824q^{49} + 52126q^{50} - 33014q^{51} - 16936q^{52} + 20724q^{53} + 3154q^{54} + 5203q^{55} - 40392q^{56} + 25920q^{57} - 7476q^{58} - 10199q^{59} - 18016q^{60} + 1506q^{61} + 5798q^{62} - 12676q^{63} + 8320q^{64} + 14144q^{65} - 32186q^{66} - 17755q^{67} - 23576q^{68} - 20593q^{69} - 122612q^{70} + 70305q^{71} - 98496q^{72} + 17350q^{73} + 105042q^{74} + 19544q^{75} + 110064q^{76} + 8954q^{77} + 56104q^{78} + 190286q^{79} + 123544q^{80} - 141268q^{81} - 249260q^{82} - 246642q^{83} + 346016q^{84} - 117074q^{85} + 259164q^{86} + 61992q^{87} - 91476q^{88} - 89409q^{89} + 102056q^{90} - 121112q^{91} - 395872q^{92} + 80023q^{93} - 103600q^{94} - 14904q^{95} + 344q^{96} + 76589q^{97} + 70308q^{98} + 1331q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
11.6.a.a \(1\) \(1.764\) \(\Q\) None \(-4\) \(-15\) \(-19\) \(10\) \(+\) \(q-4q^{2}-15q^{3}-2^{4}q^{4}-19q^{5}+60q^{6}+\cdots\)
11.6.a.b \(3\) \(1.764\) 3.3.54492.1 None \(0\) \(34\) \(24\) \(84\) \(-\) \(q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 4 T + 32 T^{2} \))(\( 1 + 6 T^{2} + 188 T^{3} + 192 T^{4} + 32768 T^{6} \))
$3$ (\( 1 + 15 T + 243 T^{2} \))(\( 1 - 34 T + 946 T^{2} - 15312 T^{3} + 229878 T^{4} - 2007666 T^{5} + 14348907 T^{6} \))
$5$ (\( 1 + 19 T + 3125 T^{2} \))(\( 1 - 24 T + 5004 T^{2} - 111046 T^{3} + 15637500 T^{4} - 234375000 T^{5} + 30517578125 T^{6} \))
$7$ (\( 1 - 10 T + 16807 T^{2} \))(\( 1 - 84 T + 4473 T^{2} + 2556872 T^{3} + 75177711 T^{4} - 23727920916 T^{5} + 4747561509943 T^{6} \))
$11$ (\( 1 + 121 T \))(\( ( 1 - 121 T )^{3} \))
$13$ (\( 1 + 1148 T + 371293 T^{2} \))(\( 1 - 486 T + 767415 T^{2} - 196760188 T^{3} + 284935817595 T^{4} - 66999227038614 T^{5} + 51185893014090757 T^{6} \))
$17$ (\( 1 - 686 T + 1419857 T^{2} \))(\( 1 - 1086 T + 2690223 T^{2} - 2752177348 T^{3} + 3819731958111 T^{4} - 2189369375887614 T^{5} + 2862423051509815793 T^{6} \))
$19$ (\( 1 + 384 T + 2476099 T^{2} \))(\( 1 - 1380 T + 7644297 T^{2} - 6777009240 T^{3} + 18928036157403 T^{4} - 8460871435765380 T^{5} + 15181127029874798299 T^{6} \))
$23$ (\( 1 - 3709 T + 6436343 T^{2} \))(\( 1 + 3066 T + 8993526 T^{2} + 22463329348 T^{3} + 57885418115418 T^{4} + 127013683381047834 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))
$29$ (\( 1 + 5424 T + 20511149 T^{2} \))(\( 1 + 3426 T + 62121159 T^{2} + 136513203828 T^{3} + 1274176348301691 T^{4} + 1441342981286488626 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))
$31$ (\( 1 + 6443 T + 28629151 T^{2} \))(\( 1 + 4098 T + 90136878 T^{2} + 235738865996 T^{3} + 2580542290930578 T^{4} + 3358836720047322498 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))
$37$ (\( 1 - 12063 T + 69343957 T^{2} \))(\( 1 - 17724 T + 229846956 T^{2} - 1916316420702 T^{3} + 15938497433444892 T^{4} - 85227349416733955676 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))
$41$ (\( 1 + 1528 T + 115856201 T^{2} \))(\( 1 - 5994 T + 174379803 T^{2} - 1186954316020 T^{3} + 20202981506708403 T^{4} - 80455419905053491594 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))
$43$ (\( 1 + 4026 T + 147008443 T^{2} \))(\( 1 + 26208 T + 443706117 T^{2} + 5261719449744 T^{3} + 65228545409745831 T^{4} + \)\(56\!\cdots\!92\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))
$47$ (\( 1 - 7168 T + 229345007 T^{2} \))(\( 1 + 17232 T + 689784333 T^{2} + 7833971382112 T^{3} + 158198592680375331 T^{4} + \)\(90\!\cdots\!68\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))
$53$ (\( 1 + 29862 T + 418195493 T^{2} \))(\( 1 - 50586 T + 1969881291 T^{2} - 44160585727452 T^{3} + 823795477641221463 T^{4} - \)\(88\!\cdots\!14\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))
$59$ (\( 1 + 6461 T + 714924299 T^{2} \))(\( 1 + 3738 T + 1293303186 T^{2} + 13104411496384 T^{3} + 924613873645516614 T^{4} + \)\(19\!\cdots\!38\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))
$61$ (\( 1 + 16980 T + 844596301 T^{2} \))(\( 1 - 18486 T + 1754869767 T^{2} - 15992539689564 T^{3} + 1482156513944931867 T^{4} - \)\(13\!\cdots\!86\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))
$67$ (\( 1 - 29999 T + 1350125107 T^{2} \))(\( 1 + 47754 T + 997454514 T^{2} - 18340812610856 T^{3} + 1346688382441882998 T^{4} + \)\(87\!\cdots\!46\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))
$71$ (\( 1 - 31023 T + 1804229351 T^{2} \))(\( 1 - 39282 T + 4433022990 T^{2} - 143037873283668 T^{3} + 7998190192215779490 T^{4} - \)\(12\!\cdots\!82\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))
$73$ (\( 1 - 1924 T + 2073071593 T^{2} \))(\( 1 - 15426 T + 2562304635 T^{2} - 98498106053188 T^{3} + 5311840951430733555 T^{4} - \)\(66\!\cdots\!74\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))
$79$ (\( 1 - 65138 T + 3077056399 T^{2} \))(\( 1 - 125148 T + 13122635793 T^{2} - 768895025227784 T^{3} + 40379090438597089407 T^{4} - \)\(11\!\cdots\!48\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))
$83$ (\( 1 + 102714 T + 3939040643 T^{2} \))(\( 1 + 143928 T + 12127124157 T^{2} + 722278658611584 T^{3} + 47769234937130112951 T^{4} + \)\(22\!\cdots\!72\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))
$89$ (\( 1 - 17415 T + 5584059449 T^{2} \))(\( 1 + 106824 T + 17674467768 T^{2} + 1102702152985302 T^{3} + 98695278745946339832 T^{4} + \)\(33\!\cdots\!24\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))
$97$ (\( 1 - 66905 T + 8587340257 T^{2} \))(\( 1 - 9684 T + 23649435576 T^{2} - 176541508624682 T^{3} + \)\(20\!\cdots\!32\)\( T^{4} - \)\(71\!\cdots\!16\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))
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