Properties

Label 8.4.b
Level $8$
Weight $4$
Character orbit 8.b
Rep. character $\chi_{8}(5,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.4.b.a 8.b 8.b $2$ $0.472$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)