Properties

Label 117.2.l
Level $117$
Weight $2$
Character orbit 117.l
Rep. character $\chi_{117}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $2$
Sturm bound $28$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 117.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(117, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 24 24 0
Eisenstein series 8 8 0

Trace form

\( 24 q - q^{3} - 22 q^{4} - 12 q^{6} - 3 q^{7} + q^{9} - 4 q^{10} - 11 q^{12} - 2 q^{13} - 6 q^{14} - 9 q^{15} + 14 q^{16} + 6 q^{17} + 30 q^{18} - 9 q^{19} - 27 q^{20} - 15 q^{21} + 14 q^{22} + 9 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(117, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
117.2.l.a 117.l 117.l $2$ $0.934$ \(\Q(\sqrt{-3}) \) None 117.2.l.a \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots\)
117.2.l.b 117.l 117.l $22$ $0.934$ None 117.2.l.b \(0\) \(-1\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{6}]$