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Properties

Label 138.4.d
Level $138$
Weight $4$
Character orbit 138.d
Rep. character $\chi_{138}(137,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 138.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(138, [\chi])\).

Total New Old
Modular forms 76 24 52
Cusp forms 68 24 44
Eisenstein series 8 0 8

Trace form

\( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} + O(q^{10}) \) \( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} - 32 q^{12} + 96 q^{13} + 384 q^{16} + 128 q^{18} - 32 q^{24} + 144 q^{25} + 188 q^{27} + 72 q^{31} - 144 q^{36} - 660 q^{39} - 96 q^{46} + 128 q^{48} - 504 q^{49} - 384 q^{52} + 88 q^{54} - 672 q^{55} + 816 q^{58} - 1536 q^{64} + 352 q^{69} + 624 q^{70} - 512 q^{72} - 2688 q^{73} - 1072 q^{75} + 80 q^{78} - 2356 q^{81} + 1344 q^{82} + 4872 q^{85} + 3748 q^{87} - 2924 q^{93} - 1296 q^{94} + 128 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.4.d.a 138.d 69.c $24$ $8.142$ None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

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