Properties

Label 8.10.b
Level 88
Weight 1010
Character orbit 8.b
Rep. character χ8(5,)\chi_{8}(5,\cdot)
Character field Q\Q
Dimension 88
Newform subspaces 11
Sturm bound 1010
Trace bound 00

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Defining parameters

Level: N N == 8=23 8 = 2^{3}
Weight: k k == 10 10
Character orbit: [χ][\chi] == 8.b (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 8 8
Character field: Q\Q
Newform subspaces: 1 1
Sturm bound: 1010
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M10(8,[χ])M_{10}(8, [\chi]).

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

Trace form

8q18q2428q4+4684q6+4800q73384q839368q9+26392q10+54760q1272336q14163136q15+185616q16102000q1723614q18+1245264q20+3062604162q98+O(q100) 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9} + 26392 q^{10} + 54760 q^{12} - 72336 q^{14} - 163136 q^{15} + 185616 q^{16} - 102000 q^{17} - 23614 q^{18} + 1245264 q^{20}+ \cdots - 3062604162 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S10new(8,[χ])S_{10}^{\mathrm{new}}(8, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
8.10.b.a 8.b 8.b 88 4.1204.120 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 8.10.b.a 18-18 00 00 48004800 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(2β1)q2+(β1+β3)q3+(54+)q4+q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots