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Properties

Label 45.8.j
Level $45$
Weight $8$
Character orbit 45.j
Rep. character $\chi_{45}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
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 88 88 0
Cusp forms 80 80 0
Eisenstein series 8 8 0

Trace form

\( 80 q + 2430 q^{4} - 72 q^{5} - 1188 q^{6} - 2556 q^{9} - 260 q^{10} + 7692 q^{11} - 31410 q^{14} + 11808 q^{15} - 139010 q^{16} - 8 q^{19} + 94674 q^{20} + 32700 q^{21} + 220878 q^{24} + 35996 q^{25} - 276312 q^{26}+ \cdots - 9419148 q^{99}+O(q^{100}) \) 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.j.a 45.j 45.j $80$ $14.057$ None 45.8.j.a \(0\) \(0\) \(-72\) \(0\) $\mathrm{SU}(2)[C_{6}]$