Properties

Label 11.3.d
Level 11
Weight 3
Character orbit d
Rep. character \(\chi_{11}(2,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 4
Newform subspaces 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 11.d (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(11, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\( 4q - 5q^{2} - 9q^{4} - 4q^{5} + 15q^{6} + 10q^{7} + 15q^{8} - 11q^{9} + O(q^{10}) \) \( 4q - 5q^{2} - 9q^{4} - 4q^{5} + 15q^{6} + 10q^{7} + 15q^{8} - 11q^{9} + q^{11} - 30q^{12} - 20q^{13} - 10q^{14} + 19q^{16} + 30q^{18} + 25q^{19} + 44q^{20} - 35q^{22} - 20q^{23} + 5q^{24} + 9q^{25} - 10q^{26} + 15q^{27} - 60q^{28} - 40q^{29} - 80q^{30} - 58q^{31} + 65q^{33} + 130q^{34} + 80q^{35} + 26q^{36} + 90q^{37} - 60q^{38} + 50q^{39} - 60q^{40} - 80q^{41} - 10q^{42} + 24q^{44} - 24q^{45} + 30q^{46} - 30q^{47} - 40q^{48} - 109q^{49} - 45q^{50} - 195q^{51} + 110q^{52} + 120q^{53} - 76q^{55} + 100q^{56} + 45q^{57} + 40q^{58} + 23q^{59} + 140q^{60} + 10q^{61} + 200q^{62} + 90q^{63} - 149q^{64} + 90q^{66} - 230q^{67} - 260q^{68} - 10q^{69} - 40q^{70} + 148q^{71} - 95q^{72} + 300q^{73} - 270q^{74} + 45q^{75} - 200q^{77} - 200q^{78} + 70q^{79} - 84q^{80} - 116q^{81} + 25q^{82} + 225q^{83} + 90q^{84} + 260q^{85} + 175q^{86} + 55q^{88} + 122q^{89} - 20q^{90} - 80q^{91} + 40q^{92} - 200q^{93} + 120q^{94} - 100q^{95} + 340q^{96} - 165q^{97} + 31q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(11, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.3.d.a \(4\) \(0.300\) \(\Q(\zeta_{10})\) None \(-5\) \(0\) \(-4\) \(10\) \(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 5 T + 19 T^{2} + 55 T^{3} + 121 T^{4} + 220 T^{5} + 304 T^{6} + 320 T^{7} + 256 T^{8} \)
$3$ \( 1 + T^{2} - 20 T^{3} + 61 T^{4} - 180 T^{5} + 81 T^{6} + 6561 T^{8} \)
$5$ \( 1 + 4 T - 9 T^{2} - 136 T^{3} - 319 T^{4} - 3400 T^{5} - 5625 T^{6} + 62500 T^{7} + 390625 T^{8} \)
$7$ \( 1 - 10 T + 129 T^{2} - 1310 T^{3} + 8361 T^{4} - 64190 T^{5} + 309729 T^{6} - 1176490 T^{7} + 5764801 T^{8} \)
$11$ \( 1 - T - 209 T^{2} - 121 T^{3} + 14641 T^{4} \)
$13$ \( 1 + 20 T + 369 T^{2} + 6070 T^{3} + 81261 T^{4} + 1025830 T^{5} + 10539009 T^{6} + 96536180 T^{7} + 815730721 T^{8} \)
$17$ \( 1 + 289 T^{2} + 7800 T^{3} - 17879 T^{4} + 2254200 T^{5} + 24137569 T^{6} + 6975757441 T^{8} \)
$19$ \( 1 - 25 T + 561 T^{2} - 5855 T^{3} + 141756 T^{4} - 2113655 T^{5} + 73110081 T^{6} - 1176147025 T^{7} + 16983563041 T^{8} \)
$23$ \( ( 1 + 10 T + 1078 T^{2} + 5290 T^{3} + 279841 T^{4} )^{2} \)
$29$ \( 1 + 40 T + 1881 T^{2} + 81410 T^{3} + 2180301 T^{4} + 68465810 T^{5} + 1330395561 T^{6} + 23792932840 T^{7} + 500246412961 T^{8} \)
$31$ \( 1 + 58 T + 423 T^{2} - 17434 T^{3} - 243175 T^{4} - 16754074 T^{5} + 390649383 T^{6} + 51475213498 T^{7} + 852891037441 T^{8} \)
$37$ \( 1 - 90 T + 3491 T^{2} - 145800 T^{3} + 6716341 T^{4} - 199600200 T^{5} + 6542696051 T^{6} - 230915376810 T^{7} + 3512479453921 T^{8} \)
$41$ \( 1 + 80 T + 6401 T^{2} + 349320 T^{3} + 15534121 T^{4} + 587206920 T^{5} + 18087696161 T^{6} + 380008339280 T^{7} + 7984925229121 T^{8} \)
$43$ \( 1 - 5771 T^{2} + 15084961 T^{4} - 19729900571 T^{6} + 11688200277601 T^{8} \)
$47$ \( 1 + 30 T - 1569 T^{2} - 98050 T^{3} + 581001 T^{4} - 216592450 T^{5} - 7656219489 T^{6} + 323376459870 T^{7} + 23811286661761 T^{8} \)
$53$ \( 1 - 120 T + 2591 T^{2} + 279810 T^{3} - 24164819 T^{4} + 785986290 T^{5} + 20444236271 T^{6} - 2659723335480 T^{7} + 62259690411361 T^{8} \)
$59$ \( 1 - 23 T - 2427 T^{2} - 104641 T^{3} + 14691380 T^{4} - 364255321 T^{5} - 29408835147 T^{6} - 970152273743 T^{7} + 146830437604321 T^{8} \)
$61$ \( 1 - 10 T + 3601 T^{2} + 243430 T^{3} + 7253641 T^{4} + 905803030 T^{5} + 49858873441 T^{6} - 515203743610 T^{7} + 191707312997281 T^{8} \)
$67$ \( ( 1 + 115 T + 11923 T^{2} + 516235 T^{3} + 20151121 T^{4} )^{2} \)
$71$ \( 1 - 148 T + 9423 T^{2} - 841046 T^{3} + 82451165 T^{4} - 4239712886 T^{5} + 239454270063 T^{6} - 18958842020308 T^{7} + 645753531245761 T^{8} \)
$73$ \( 1 - 300 T + 46429 T^{2} - 5018400 T^{3} + 415041241 T^{4} - 26743053600 T^{5} + 1318501931389 T^{6} - 45400267886700 T^{7} + 806460091894081 T^{8} \)
$79$ \( 1 - 70 T + 10021 T^{2} - 1216880 T^{3} + 75589621 T^{4} - 7594548080 T^{5} + 390318761701 T^{6} - 17016121886470 T^{7} + 1517108809906561 T^{8} \)
$83$ \( 1 - 225 T + 27589 T^{2} - 2589975 T^{3} + 221504596 T^{4} - 17842337775 T^{5} + 1309327618069 T^{6} - 73561584008025 T^{7} + 2252292232139041 T^{8} \)
$89$ \( ( 1 - 61 T + 8161 T^{2} - 483181 T^{3} + 62742241 T^{4} )^{2} \)
$97$ \( 1 + 165 T + 7431 T^{2} + 999895 T^{3} + 180445176 T^{4} + 9408012055 T^{5} + 657861087111 T^{6} + 137440380813285 T^{7} + 7837433594376961 T^{8} \)
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