Properties

Label 8.4.b
Level 8
Weight 4
Character orbit b
Rep. character \(\chi_{8}(5,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 8.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(8, [\chi])\).

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

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 28q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut 40q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 28q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut 40q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 56q^{10} \) \(\mathstrut -\mathstrut 56q^{12} \) \(\mathstrut +\mathstrut 16q^{14} \) \(\mathstrut +\mathstrut 112q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 28q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 112q^{20} \) \(\mathstrut -\mathstrut 84q^{22} \) \(\mathstrut -\mathstrut 304q^{23} \) \(\mathstrut -\mathstrut 112q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut +\mathstrut 280q^{26} \) \(\mathstrut +\mathstrut 96q^{28} \) \(\mathstrut -\mathstrut 112q^{30} \) \(\mathstrut +\mathstrut 448q^{31} \) \(\mathstrut -\mathstrut 352q^{32} \) \(\mathstrut +\mathstrut 168q^{33} \) \(\mathstrut +\mathstrut 28q^{34} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut -\mathstrut 196q^{38} \) \(\mathstrut -\mathstrut 560q^{39} \) \(\mathstrut +\mathstrut 224q^{40} \) \(\mathstrut -\mathstrut 140q^{41} \) \(\mathstrut -\mathstrut 224q^{42} \) \(\mathstrut +\mathstrut 168q^{44} \) \(\mathstrut +\mathstrut 304q^{46} \) \(\mathstrut +\mathstrut 672q^{47} \) \(\mathstrut +\mathstrut 672q^{48} \) \(\mathstrut -\mathstrut 558q^{49} \) \(\mathstrut -\mathstrut 26q^{50} \) \(\mathstrut -\mathstrut 560q^{52} \) \(\mathstrut +\mathstrut 728q^{54} \) \(\mathstrut -\mathstrut 336q^{55} \) \(\mathstrut -\mathstrut 320q^{56} \) \(\mathstrut +\mathstrut 392q^{57} \) \(\mathstrut -\mathstrut 840q^{58} \) \(\mathstrut -\mathstrut 672q^{60} \) \(\mathstrut -\mathstrut 448q^{62} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut +\mathstrut 576q^{64} \) \(\mathstrut +\mathstrut 1120q^{65} \) \(\mathstrut -\mathstrut 168q^{66} \) \(\mathstrut +\mathstrut 168q^{68} \) \(\mathstrut +\mathstrut 448q^{70} \) \(\mathstrut -\mathstrut 144q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 588q^{73} \) \(\mathstrut +\mathstrut 1288q^{74} \) \(\mathstrut +\mathstrut 392q^{76} \) \(\mathstrut +\mathstrut 560q^{78} \) \(\mathstrut -\mathstrut 928q^{79} \) \(\mathstrut -\mathstrut 1344q^{80} \) \(\mathstrut -\mathstrut 1510q^{81} \) \(\mathstrut +\mathstrut 140q^{82} \) \(\mathstrut +\mathstrut 448q^{84} \) \(\mathstrut -\mathstrut 2324q^{86} \) \(\mathstrut +\mathstrut 1680q^{87} \) \(\mathstrut +\mathstrut 336q^{88} \) \(\mathstrut +\mathstrut 532q^{89} \) \(\mathstrut +\mathstrut 56q^{90} \) \(\mathstrut +\mathstrut 1824q^{92} \) \(\mathstrut -\mathstrut 672q^{94} \) \(\mathstrut -\mathstrut 784q^{95} \) \(\mathstrut -\mathstrut 448q^{96} \) \(\mathstrut +\mathstrut 1988q^{97} \) \(\mathstrut +\mathstrut 558q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(8, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.4.b.a \(2\) \(0.472\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-16\) \(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)