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Properties

Label 117.3.w
Level $117$
Weight $3$
Character orbit 117.w
Rep. character $\chi_{117}(58,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $104$
Newform subspaces $1$
Sturm bound $42$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 117.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(117, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

Trace form

\( 104 q - 2 q^{2} - 2 q^{3} - 2 q^{5} - 32 q^{6} + 18 q^{8} - 2 q^{9} - 12 q^{10} + 22 q^{11} + 54 q^{12} - 2 q^{13} - 4 q^{14} + 70 q^{15} - 324 q^{16} - 12 q^{17} - 86 q^{18} - 36 q^{19} + 134 q^{20} - 32 q^{21}+ \cdots + 940 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(117, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
117.3.w.a 117.w 117.w $104$ $3.188$ None 117.3.w.a \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$