Properties

Label 32.6.g
Level $32$
Weight $6$
Character orbit 32.g
Rep. character $\chi_{32}(5,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $76$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(32, [\chi])\).

Total New Old
Modular forms 84 84 0
Cusp forms 76 76 0
Eisenstein series 8 8 0

Trace form

\( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 204 q^{10} - 4 q^{11} - 1588 q^{12} - 4 q^{13} + 2476 q^{14} + 4176 q^{16} - 1624 q^{18} - 4 q^{19} - 7604 q^{20} - 4 q^{21}+ \cdots + 338544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.6.g.a 32.g 32.g $76$ $5.132$ None 32.6.g.a \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$