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Properties

Label 45.8.l
Level $45$
Weight $8$
Character orbit 45.l
Rep. character $\chi_{45}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $160$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 45.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(45, [\chi])\).

Total New Old
Modular forms 176 176 0
Cusp forms 160 160 0
Eisenstein series 16 16 0

Trace form

\( 160 q - 6 q^{2} - 30 q^{3} - 6 q^{5} + 1848 q^{6} - 2 q^{7} - 8 q^{10} + 17712 q^{11} + 2022 q^{12} - 2 q^{13} - 37566 q^{15} + 278524 q^{16} - 60480 q^{18} - 109062 q^{20} - 84156 q^{21} - 514 q^{22} - 6894 q^{23}+ \cdots + 17617708 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.8.l.a 45.l 45.l $160$ $14.057$ None 45.8.l.a \(-6\) \(-30\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{12}]$