Properties

Label 117.2.t
Level $117$
Weight $2$
Character orbit 117.t
Rep. character $\chi_{117}(25,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $3$
Sturm bound $28$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 117.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(28\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

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

\( 24 q - 4 q^{3} + 8 q^{4} + 4 q^{9} + O(q^{10}) \) \( 24 q - 4 q^{3} + 8 q^{4} + 4 q^{9} - 16 q^{10} + 10 q^{12} - 2 q^{13} - 18 q^{14} - 4 q^{16} - 24 q^{17} - 10 q^{22} + 18 q^{23} + 2 q^{25} - 12 q^{26} - 22 q^{27} - 54 q^{30} + 36 q^{35} + 26 q^{36} + 12 q^{38} - 14 q^{39} - 8 q^{40} + 6 q^{42} + 6 q^{43} + 38 q^{48} - 60 q^{51} + 4 q^{52} + 72 q^{53} - 28 q^{55} + 36 q^{56} - 16 q^{61} - 72 q^{62} + 40 q^{64} + 78 q^{66} + 36 q^{68} + 90 q^{69} - 42 q^{74} - 8 q^{75} - 30 q^{77} + 66 q^{78} - 16 q^{79} + 28 q^{81} - 4 q^{82} - 54 q^{87} + 22 q^{88} + 24 q^{90} - 24 q^{91} - 96 q^{92} + 20 q^{94} + 48 q^{95} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
117.2.t.a 117.t 117.t $2$ $0.934$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)
117.2.t.b 117.t 117.t $2$ $0.934$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots\)
117.2.t.c 117.t 117.t $20$ $0.934$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{17}q^{2}+\beta _{10}q^{3}+(1-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots\)