Properties

Label 8.10.b
Level 8
Weight 10
Character orbit b
Rep. character \(\chi_{8}(5,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 10 \)
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: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(8, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 8 8 0
Eisenstein series 2 2 0

Trace form

\( 8q - 18q^{2} - 428q^{4} + 4684q^{6} + 4800q^{7} - 3384q^{8} - 39368q^{9} + O(q^{10}) \) \( 8q - 18q^{2} - 428q^{4} + 4684q^{6} + 4800q^{7} - 3384q^{8} - 39368q^{9} + 26392q^{10} + 54760q^{12} - 72336q^{14} - 163136q^{15} + 185616q^{16} - 102000q^{17} - 23614q^{18} + 1245264q^{20} - 2373124q^{22} + 3412032q^{23} - 3961456q^{24} - 2423384q^{25} + 4551240q^{26} + 7509920q^{28} - 15284368q^{30} + 803584q^{31} - 14113248q^{32} + 58272q^{33} + 27757244q^{34} + 57226188q^{36} - 63661140q^{38} - 17590208q^{39} - 93063648q^{40} - 2180784q^{41} + 127541344q^{42} + 114013320q^{44} - 131840944q^{46} + 7432320q^{47} - 217917408q^{48} + 24436680q^{49} + 231784902q^{50} + 219270896q^{52} - 362934280q^{54} + 7056832q^{55} - 358503360q^{56} + 134003744q^{57} + 375425192q^{58} + 516952992q^{60} - 344291904q^{62} - 223198400q^{63} - 316815296q^{64} - 146501760q^{65} + 239713176q^{66} + 79875048q^{68} - 56202048q^{70} + 560234688q^{71} + 112273016q^{72} - 523987120q^{73} - 65773608q^{74} - 87532760q^{76} + 318117968q^{78} - 248943744q^{79} + 890441280q^{80} + 231960296q^{81} - 1051981172q^{82} - 1275608768q^{84} + 1492810428q^{86} + 540527424q^{87} + 1544767952q^{88} + 744827856q^{89} - 3218579800q^{90} - 2959012128q^{92} + 3068552352q^{94} - 1465245504q^{95} + 4296343616q^{96} - 9932784q^{97} - 3062604162q^{98} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.10.b.a \(8\) \(4.120\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-18\) \(0\) \(0\) \(4800\) \(q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots\)