Properties

Label 11.4.a
Level 11
Weight 4
Character orbit a
Rep. character \(\chi_{11}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 11.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(11))\).

Total New Old
Modular forms 4 2 2
Cusp forms 2 2 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.
\(+\)\(2\)

Trace form

\( 2q + 2q^{2} - 2q^{3} - 8q^{4} + 2q^{5} - 26q^{6} + 20q^{7} - 12q^{8} + 44q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 2q^{3} - 8q^{4} + 2q^{5} - 26q^{6} + 20q^{7} - 12q^{8} + 44q^{9} + 50q^{10} - 22q^{11} - 40q^{12} + 80q^{13} - 4q^{14} - 194q^{15} - 8q^{16} - 124q^{17} + 92q^{18} + 72q^{19} + 88q^{20} + 76q^{21} - 22q^{22} - 98q^{23} + 252q^{24} + 136q^{25} - 40q^{26} - 182q^{27} - 128q^{28} + 144q^{29} - 266q^{30} - 34q^{31} - 104q^{32} + 22q^{33} - 52q^{34} - 172q^{35} - 80q^{36} + 54q^{37} + 432q^{38} + 400q^{39} - 492q^{40} + 536q^{41} - 140q^{42} - 60q^{43} + 88q^{44} + 428q^{45} - 314q^{46} - 272q^{47} + 776q^{48} - 390q^{49} + 232q^{50} - 164q^{51} - 560q^{52} - 492q^{53} - 110q^{54} - 22q^{55} + 120q^{56} - 1512q^{57} - 192q^{58} + 634q^{59} + 632q^{60} + 840q^{61} + 134q^{62} + 248q^{63} + 224q^{64} - 880q^{65} + 286q^{66} + 754q^{67} + 640q^{68} + 962q^{69} + 284q^{70} - 678q^{71} - 744q^{72} - 400q^{73} + 6q^{74} - 520q^{75} + 432q^{76} - 220q^{77} - 440q^{78} + 316q^{79} - 1544q^{80} - 1294q^{81} + 512q^{82} + 468q^{83} - 736q^{84} + 452q^{85} - 156q^{86} + 1200q^{87} + 132q^{88} - 1842q^{89} + 1532q^{90} + 1280q^{91} - 40q^{92} - 638q^{93} - 992q^{94} + 2952q^{95} - 952q^{96} + 2194q^{97} - 870q^{98} - 484q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
11.4.a.a \(2\) \(0.649\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(20\) \(+\) \(q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T + 14 T^{2} - 16 T^{3} + 64 T^{4} \)
$3$ \( 1 + 2 T + 7 T^{2} + 54 T^{3} + 729 T^{4} \)
$5$ \( 1 - 2 T + 59 T^{2} - 250 T^{3} + 15625 T^{4} \)
$7$ \( 1 - 20 T + 738 T^{2} - 6860 T^{3} + 117649 T^{4} \)
$11$ \( ( 1 + 11 T )^{2} \)
$13$ \( 1 - 80 T + 4794 T^{2} - 175760 T^{3} + 4826809 T^{4} \)
$17$ \( 1 + 124 T + 13238 T^{2} + 609212 T^{3} + 24137569 T^{4} \)
$19$ \( 1 - 72 T + 4214 T^{2} - 493848 T^{3} + 47045881 T^{4} \)
$23$ \( 1 + 98 T + 22847 T^{2} + 1192366 T^{3} + 148035889 T^{4} \)
$29$ \( 1 - 144 T + 44554 T^{2} - 3512016 T^{3} + 594823321 T^{4} \)
$31$ \( 1 + 34 T + 57519 T^{2} + 1012894 T^{3} + 887503681 T^{4} \)
$37$ \( 1 - 54 T + 101843 T^{2} - 2735262 T^{3} + 2565726409 T^{4} \)
$41$ \( 1 - 536 T + 209618 T^{2} - 36941656 T^{3} + 4750104241 T^{4} \)
$43$ \( 1 + 60 T + 159146 T^{2} + 4770420 T^{3} + 6321363049 T^{4} \)
$47$ \( 1 + 272 T + 182942 T^{2} + 28239856 T^{3} + 10779215329 T^{4} \)
$53$ \( 1 + 492 T + 348862 T^{2} + 73247484 T^{3} + 22164361129 T^{4} \)
$59$ \( 1 - 634 T + 458975 T^{2} - 130210286 T^{3} + 42180533641 T^{4} \)
$61$ \( 1 - 840 T + 528794 T^{2} - 190664040 T^{3} + 51520374361 T^{4} \)
$67$ \( 1 - 754 T + 742455 T^{2} - 226775302 T^{3} + 90458382169 T^{4} \)
$71$ \( 1 + 678 T + 813415 T^{2} + 242663658 T^{3} + 128100283921 T^{4} \)
$73$ \( 1 + 400 T + 160962 T^{2} + 155606800 T^{3} + 151334226289 T^{4} \)
$79$ \( 1 - 316 T - 279966 T^{2} - 155800324 T^{3} + 243087455521 T^{4} \)
$83$ \( 1 - 468 T + 1155130 T^{2} - 267596316 T^{3} + 326940373369 T^{4} \)
$89$ \( 1 + 1842 T + 1935427 T^{2} + 1298552898 T^{3} + 496981290961 T^{4} \)
$97$ \( 1 - 2194 T + 2966547 T^{2} - 2002404562 T^{3} + 832972004929 T^{4} \)
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