Properties

Label 138.2.f
Level $138$
Weight $2$
Character orbit 138.f
Rep. character $\chi_{138}(5,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $80$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 138.f (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(138, [\chi])\).

Total New Old
Modular forms 280 80 200
Cusp forms 200 80 120
Eisenstein series 80 0 80

Trace form

\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} + O(q^{10}) \) \( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.2.f.a 138.f 69.g $80$ $1.102$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(138, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)