Properties

Label 9.3.d
Level $9$
Weight $3$
Character orbit 9.d
Rep. character $\chi_{9}(2,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(9, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\( 2 q - 3 q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 9 q^{6} - 2 q^{7} - 9 q^{9} - 12 q^{10} - 3 q^{11} + 6 q^{12} + 4 q^{13} + 6 q^{14} + 11 q^{16} + 22 q^{19} - 6 q^{20} - 6 q^{21} + 3 q^{22} - 48 q^{23} - 45 q^{24}+ \cdots + 115 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.3.d.a 9.d 9.d $2$ $0.245$ \(\Q(\sqrt{-3}) \) None 9.3.d.a \(-3\) \(-3\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)