Properties

Label 138.6.d
Level $138$
Weight $6$
Character orbit 138.d
Rep. character $\chi_{138}(137,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(138, [\chi])\).

Total New Old
Modular forms 124 40 84
Cusp forms 116 40 76
Eisenstein series 8 0 8

Trace form

\( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9} + O(q^{10}) \) \( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9} + 64 q^{12} - 1048 q^{13} + 10240 q^{16} + 1280 q^{18} - 1280 q^{24} + 30480 q^{25} + 1700 q^{27} - 22576 q^{31} - 8064 q^{36} + 55608 q^{39} + 1088 q^{46} - 1024 q^{48} - 23224 q^{49} + 16768 q^{52} + 25456 q^{54} + 210400 q^{55} - 83168 q^{58} - 163840 q^{64} + 99076 q^{69} + 167520 q^{70} - 20480 q^{72} + 241160 q^{73} - 255604 q^{75} - 233440 q^{78} + 78512 q^{81} - 8832 q^{82} - 460296 q^{85} - 4136 q^{87} + 500704 q^{93} - 138272 q^{94} + 20480 q^{96} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.6.d.a 138.d 69.c $40$ $22.133$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(138, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)