Properties

Label 117.4.z
Level $117$
Weight $4$
Character orbit 117.z
Rep. character $\chi_{117}(5,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $160$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.z (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(117, [\chi])\).

Total New Old
Modular forms 176 176 0
Cusp forms 160 160 0
Eisenstein series 16 16 0

Trace form

\( 160 q - 6 q^{2} - 8 q^{3} - 6 q^{5} - 50 q^{6} + 10 q^{7} - 8 q^{9} + 18 q^{11} - 2 q^{13} - 12 q^{14} - 194 q^{15} + 1084 q^{16} - 302 q^{18} + 112 q^{19} + 42 q^{20} + 82 q^{21} - 4 q^{22} + 840 q^{24}+ \cdots - 2042 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(117, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
117.4.z.a 117.z 117.z $160$ $6.903$ None 117.4.z.a \(-6\) \(-8\) \(-6\) \(10\) $\mathrm{SU}(2)[C_{12}]$