Properties

Label 8.6.b
Level $8$
Weight $6$
Character orbit 8.b
Rep. character $\chi_{8}(5,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

\( 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9} + 632 q^{10} + 1576 q^{12} - 2384 q^{14} - 416 q^{15} - 3312 q^{16} + 200 q^{17} + 4754 q^{18} + 4624 q^{20} - 5636 q^{22} + 2336 q^{23}+ \cdots - 117042 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.6.b.a 8.b 8.b $4$ $1.283$ 4.0.218489.1 None 8.6.b.a \(-2\) \(0\) \(0\) \(96\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)