Properties

Label 8.6.b
Level 8
Weight 6
Character orbit b
Rep. character \(\chi_{8}(5,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 8.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(8, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 4 4 0
Eisenstein series 2 2 0

Trace form

\( 4q - 2q^{2} + 20q^{4} - 116q^{6} + 96q^{7} - 248q^{8} - 164q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 20q^{4} - 116q^{6} + 96q^{7} - 248q^{8} - 164q^{9} + 632q^{10} + 1576q^{12} - 2384q^{14} - 416q^{15} - 3312q^{16} + 200q^{17} + 4754q^{18} + 4624q^{20} - 5636q^{22} + 2336q^{23} - 7792q^{24} + 1556q^{25} + 5608q^{26} + 5152q^{28} - 2128q^{30} - 12928q^{31} + 5408q^{32} - 2352q^{33} - 4772q^{34} - 10164q^{36} + 15980q^{38} + 35104q^{39} + 16032q^{40} - 4568q^{41} - 26144q^{42} - 29112q^{44} + 29200q^{46} - 54720q^{47} + 35616q^{48} + 9828q^{49} - 47498q^{50} - 36560q^{52} + 23288q^{54} + 85472q^{55} + 40768q^{56} - 2032q^{57} + 3784q^{58} + 2592q^{60} + 34496q^{62} - 153440q^{63} - 41920q^{64} - 19520q^{65} + 43224q^{66} + 10344q^{68} - 68928q^{70} + 206688q^{71} - 83272q^{72} + 39976q^{73} + 17464q^{74} + 99944q^{76} - 174064q^{78} - 247872q^{79} - 35520q^{80} + 29684q^{81} + 161132q^{82} + 196672q^{84} - 18500q^{86} + 307872q^{87} - 167216q^{88} - 84632q^{89} + 142280q^{90} - 49056q^{92} - 98784q^{94} - 259744q^{95} - 115648q^{96} - 99576q^{97} - 117042q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(8, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.6.b.a \(4\) \(1.283\) 4.0.218489.1 None \(-2\) \(0\) \(0\) \(96\) \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)