Properties

Label 18.3.d
Level $18$
Weight $3$
Character orbit 18.d
Rep. character $\chi_{18}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 18.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(18, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q + 4 q^{4} - 18 q^{5} - 12 q^{6} + 2 q^{7} + 12 q^{9} + 18 q^{11} + 12 q^{12} - 10 q^{13} + 36 q^{14} + 18 q^{15} - 8 q^{16} - 24 q^{18} - 40 q^{19} - 36 q^{20} - 42 q^{21} - 12 q^{22} + 18 q^{23} + 4 q^{25}+ \cdots + 126 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.3.d.a 18.d 9.d $4$ $0.490$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 18.3.d.a \(0\) \(0\) \(-18\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)