Properties

Label 11.4.a
Level 11
Weight 4
Character orbit a
Rep. character \(\chi_{11}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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.

\(11\)Dim.
\(+\)\(2\)

Trace form

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\) into irreducible Hecke orbits

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 \(2\) \(-2\) \(2\) \(20\) \(+\) \(q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots\)