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Properties

Label 138.8.d
Level $138$
Weight $8$
Character orbit 138.d
Rep. character $\chi_{138}(137,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
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: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(138, [\chi])\).

Total New Old
Modular forms 172 56 116
Cusp forms 164 56 108
Eisenstein series 8 0 8

Trace form

\( 56 q - 52 q^{3} - 3584 q^{4} - 928 q^{6} - 2808 q^{9} + O(q^{10}) \) \( 56 q - 52 q^{3} - 3584 q^{4} - 928 q^{6} - 2808 q^{9} + 3328 q^{12} + 9976 q^{13} + 229376 q^{16} - 55168 q^{18} + 59392 q^{24} + 603984 q^{25} + 56564 q^{27} + 867760 q^{31} + 179712 q^{36} - 2338104 q^{39} - 1175936 q^{46} - 212992 q^{48} - 13409192 q^{49} - 638464 q^{52} + 2037088 q^{54} - 2209792 q^{55} + 1705664 q^{58} - 14680064 q^{64} - 8006564 q^{69} - 8819136 q^{70} + 3530752 q^{72} + 1955896 q^{73} - 2119732 q^{75} + 2325632 q^{78} - 8860384 q^{81} - 13670400 q^{82} + 22448712 q^{85} - 16147112 q^{87} - 20431184 q^{93} - 9890368 q^{94} - 3801088 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.8.d.a 138.d 69.c $56$ $43.109$ None \(0\) \(-52\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{8}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(138, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)