Properties

Label 11.8.a
Level 11
Weight 8
Character orbit a
Rep. character \(\chi_{11}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 2
Sturm bound 8
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 11.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(11))\).

Total New Old
Modular forms 8 6 2
Cusp forms 6 6 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.
\(+\)\(4\)
\(-\)\(2\)

Trace form

\(6q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 41q^{3} \) \(\mathstrut +\mathstrut 500q^{4} \) \(\mathstrut +\mathstrut 67q^{5} \) \(\mathstrut +\mathstrut 862q^{6} \) \(\mathstrut -\mathstrut 1058q^{7} \) \(\mathstrut +\mathstrut 60q^{8} \) \(\mathstrut +\mathstrut 1787q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 41q^{3} \) \(\mathstrut +\mathstrut 500q^{4} \) \(\mathstrut +\mathstrut 67q^{5} \) \(\mathstrut +\mathstrut 862q^{6} \) \(\mathstrut -\mathstrut 1058q^{7} \) \(\mathstrut +\mathstrut 60q^{8} \) \(\mathstrut +\mathstrut 1787q^{9} \) \(\mathstrut +\mathstrut 5750q^{10} \) \(\mathstrut -\mathstrut 2662q^{11} \) \(\mathstrut -\mathstrut 28288q^{12} \) \(\mathstrut +\mathstrut 4594q^{13} \) \(\mathstrut -\mathstrut 15236q^{14} \) \(\mathstrut -\mathstrut 6149q^{15} \) \(\mathstrut +\mathstrut 46376q^{16} \) \(\mathstrut +\mathstrut 45832q^{17} \) \(\mathstrut -\mathstrut 66886q^{18} \) \(\mathstrut +\mathstrut 32564q^{19} \) \(\mathstrut +\mathstrut 21128q^{20} \) \(\mathstrut +\mathstrut 46906q^{21} \) \(\mathstrut -\mathstrut 10648q^{22} \) \(\mathstrut -\mathstrut 70501q^{23} \) \(\mathstrut +\mathstrut 245964q^{24} \) \(\mathstrut +\mathstrut 24731q^{25} \) \(\mathstrut -\mathstrut 250916q^{26} \) \(\mathstrut -\mathstrut 135695q^{27} \) \(\mathstrut -\mathstrut 490704q^{28} \) \(\mathstrut +\mathstrut 413118q^{29} \) \(\mathstrut -\mathstrut 256826q^{30} \) \(\mathstrut +\mathstrut 132691q^{31} \) \(\mathstrut +\mathstrut 11192q^{32} \) \(\mathstrut +\mathstrut 38599q^{33} \) \(\mathstrut +\mathstrut 488q^{34} \) \(\mathstrut +\mathstrut 639478q^{35} \) \(\mathstrut +\mathstrut 815092q^{36} \) \(\mathstrut -\mathstrut 749803q^{37} \) \(\mathstrut -\mathstrut 801480q^{38} \) \(\mathstrut -\mathstrut 1384652q^{39} \) \(\mathstrut +\mathstrut 1781268q^{40} \) \(\mathstrut +\mathstrut 6226q^{41} \) \(\mathstrut +\mathstrut 1680964q^{42} \) \(\mathstrut +\mathstrut 980414q^{43} \) \(\mathstrut -\mathstrut 942348q^{44} \) \(\mathstrut -\mathstrut 1851892q^{45} \) \(\mathstrut +\mathstrut 4279846q^{46} \) \(\mathstrut -\mathstrut 66568q^{47} \) \(\mathstrut -\mathstrut 7055896q^{48} \) \(\mathstrut +\mathstrut 53706q^{49} \) \(\mathstrut -\mathstrut 3252718q^{50} \) \(\mathstrut +\mathstrut 617266q^{51} \) \(\mathstrut +\mathstrut 1514952q^{52} \) \(\mathstrut +\mathstrut 2715144q^{53} \) \(\mathstrut +\mathstrut 6445090q^{54} \) \(\mathstrut -\mathstrut 1340317q^{55} \) \(\mathstrut -\mathstrut 6062760q^{56} \) \(\mathstrut +\mathstrut 3819120q^{57} \) \(\mathstrut -\mathstrut 1046220q^{58} \) \(\mathstrut -\mathstrut 7119907q^{59} \) \(\mathstrut +\mathstrut 752912q^{60} \) \(\mathstrut -\mathstrut 5708566q^{61} \) \(\mathstrut +\mathstrut 6940534q^{62} \) \(\mathstrut +\mathstrut 859244q^{63} \) \(\mathstrut +\mathstrut 10607904q^{64} \) \(\mathstrut +\mathstrut 5688520q^{65} \) \(\mathstrut -\mathstrut 3000074q^{66} \) \(\mathstrut -\mathstrut 3542943q^{67} \) \(\mathstrut +\mathstrut 18917816q^{68} \) \(\mathstrut +\mathstrut 4250597q^{69} \) \(\mathstrut -\mathstrut 18308116q^{70} \) \(\mathstrut -\mathstrut 4568007q^{71} \) \(\mathstrut -\mathstrut 26184720q^{72} \) \(\mathstrut +\mathstrut 12352174q^{73} \) \(\mathstrut -\mathstrut 13520406q^{74} \) \(\mathstrut +\mathstrut 9979160q^{75} \) \(\mathstrut +\mathstrut 6867104q^{76} \) \(\mathstrut -\mathstrut 1860738q^{77} \) \(\mathstrut +\mathstrut 1427848q^{78} \) \(\mathstrut +\mathstrut 4367742q^{79} \) \(\mathstrut +\mathstrut 1481336q^{80} \) \(\mathstrut -\mathstrut 10193266q^{81} \) \(\mathstrut -\mathstrut 1752916q^{82} \) \(\mathstrut -\mathstrut 6503706q^{83} \) \(\mathstrut +\mathstrut 14049200q^{84} \) \(\mathstrut +\mathstrut 3504482q^{85} \) \(\mathstrut -\mathstrut 5562708q^{86} \) \(\mathstrut -\mathstrut 9064920q^{87} \) \(\mathstrut +\mathstrut 1197900q^{88} \) \(\mathstrut +\mathstrut 4783221q^{89} \) \(\mathstrut +\mathstrut 13795712q^{90} \) \(\mathstrut +\mathstrut 3752424q^{91} \) \(\mathstrut -\mathstrut 7320368q^{92} \) \(\mathstrut -\mathstrut 1131947q^{93} \) \(\mathstrut -\mathstrut 15632q^{94} \) \(\mathstrut -\mathstrut 4528968q^{95} \) \(\mathstrut +\mathstrut 19662920q^{96} \) \(\mathstrut +\mathstrut 11357247q^{97} \) \(\mathstrut +\mathstrut 24721536q^{98} \) \(\mathstrut -\mathstrut 2474329q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(11))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
11.8.a.a \(2\) \(3.436\) \(\Q(\sqrt{15}) \) None \(-8\) \(-6\) \(-470\) \(-1228\) \(-\) \(q+(-4+\beta )q^{2}+(-3-6\beta )q^{3}+(-52+\cdots)q^{4}+\cdots\)
11.8.a.b \(4\) \(3.436\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-35\) \(537\) \(170\) \(+\) \(q-\beta _{2}q^{2}+(-9-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)