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Properties

Label 138.8.f
Level $138$
Weight $8$
Character orbit 138.f
Rep. character $\chi_{138}(5,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $560$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 138.f (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(192\)

Dimensions

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

Total New Old
Modular forms 1720 560 1160
Cusp forms 1640 560 1080
Eisenstein series 80 0 80

Trace form

\( 560 q + 52 q^{3} + 3584 q^{4} + 928 q^{6} + 2808 q^{9} + O(q^{10}) \) \( 560 q + 52 q^{3} + 3584 q^{4} + 928 q^{6} + 2808 q^{9} - 3328 q^{12} - 9976 q^{13} - 7678 q^{15} - 229376 q^{16} - 223264 q^{18} + 443454 q^{21} - 59392 q^{24} - 603984 q^{25} - 1437086 q^{27} + 1480864 q^{30} - 867760 q^{31} - 2430406 q^{33} - 179712 q^{36} + 905212 q^{37} + 2338104 q^{39} + 1694308 q^{43} + 1175936 q^{46} + 212992 q^{48} + 6251756 q^{49} + 638464 q^{52} + 7400208 q^{54} + 1104688 q^{55} - 15017838 q^{57} - 5080992 q^{58} + 4394368 q^{60} + 22205656 q^{61} + 18045830 q^{63} + 14680064 q^{64} - 16558784 q^{66} - 12063172 q^{67} - 25025006 q^{69} - 11503232 q^{70} - 1931264 q^{72} + 6748756 q^{73} + 62063176 q^{75} + 15880336 q^{78} + 2313784 q^{79} - 61237116 q^{81} - 24388192 q^{82} - 11057024 q^{84} + 1978724 q^{85} + 18730550 q^{87} + 20431184 q^{93} + 9890368 q^{94} + 3801088 q^{96} + 127720956 q^{97} - 67841994 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

The newforms in this space have not yet been added to the LMFDB.

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

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