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Properties

Label 138.3.b
Level $138$
Weight $3$
Character orbit 138.b
Rep. character $\chi_{138}(91,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 138.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(138, [\chi])\).

Total New Old
Modular forms 52 8 44
Cusp forms 44 8 36
Eisenstein series 8 0 8

Trace form

\( 8 q + 16 q^{4} + 24 q^{9} + O(q^{10}) \) \( 8 q + 16 q^{4} + 24 q^{9} + 16 q^{13} + 32 q^{16} + 16 q^{23} + 72 q^{25} + 32 q^{26} - 144 q^{29} - 128 q^{31} - 112 q^{35} + 48 q^{36} + 48 q^{39} - 16 q^{41} - 80 q^{46} - 112 q^{47} + 40 q^{49} - 160 q^{50} + 32 q^{52} - 64 q^{55} + 128 q^{58} + 80 q^{59} - 96 q^{62} + 64 q^{64} - 72 q^{69} - 144 q^{70} + 32 q^{71} + 64 q^{73} + 48 q^{75} + 224 q^{77} - 144 q^{78} + 72 q^{81} + 48 q^{85} + 96 q^{87} + 32 q^{92} + 192 q^{93} - 16 q^{94} + 112 q^{95} + 224 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.3.b.a 138.b 23.b $8$ $3.760$ 8.0.1358954496.3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{2}+2\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(138, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)