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Properties

Label 45.5.i
Level $45$
Weight $5$
Character orbit 45.i
Rep. character $\chi_{45}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
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.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
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 52 32 20
Cusp forms 44 32 12
Eisenstein series 8 0 8

Trace form

\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 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.i.a 45.i 9.d $32$ $4.652$ None 45.5.i.a \(0\) \(-8\) \(0\) \(-26\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{5}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)