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Properties

Label 234.2.y
Level $234$
Weight $2$
Character orbit 234.y
Rep. character $\chi_{234}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 234.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(234, [\chi])\).

Total New Old
Modular forms 184 56 128
Cusp forms 152 56 96
Eisenstein series 32 0 32

Trace form

\( 56 q + 4 q^{7} + O(q^{10}) \) \( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(234, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
234.2.y.a 234.y 117.x $56$ $1.868$ None 234.2.y.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)