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Properties

Label 45.5.k
Level $45$
Weight $5$
Character orbit 45.k
Rep. character $\chi_{45}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $88$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 45.k (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(45, [\chi])\).

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 120 q^{6} - 2 q^{7} - 72 q^{8} - 8 q^{10} - 160 q^{11} + 186 q^{12} - 2 q^{13} + 270 q^{15} + 2044 q^{16} - 908 q^{17} - 1656 q^{18} - 834 q^{20} - 1428 q^{21} + 62 q^{22}+ \cdots + 193724 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.5.k.a 45.k 45.k $88$ $4.652$ None 45.5.k.a \(-2\) \(6\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$