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Properties

Label 1666.2.x
Level $1666$
Weight $2$
Character orbit 1666.x
Rep. character $\chi_{1666}(183,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1008$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1666.x (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1666, [\chi])\).

Total New Old
Modular forms 3072 1008 2064
Cusp forms 2976 1008 1968
Eisenstein series 96 0 96

Trace form

\( 1008 q + 168 q^{4} - 8 q^{5} + 4 q^{7} + O(q^{10}) \) \( 1008 q + 168 q^{4} - 8 q^{5} + 4 q^{7} + 20 q^{11} + 8 q^{13} - 4 q^{14} - 168 q^{16} - 8 q^{17} - 16 q^{18} - 20 q^{20} - 16 q^{21} - 8 q^{22} + 68 q^{23} - 60 q^{27} - 4 q^{28} + 24 q^{29} + 16 q^{31} + 16 q^{33} + 16 q^{34} + 24 q^{35} - 16 q^{37} + 40 q^{38} + 24 q^{39} + 16 q^{41} + 8 q^{44} - 124 q^{45} - 40 q^{47} - 16 q^{50} - 8 q^{52} - 24 q^{54} - 80 q^{55} + 4 q^{56} - 60 q^{57} + 40 q^{58} + 16 q^{61} - 44 q^{62} + 12 q^{63} + 168 q^{64} + 56 q^{65} - 16 q^{67} + 8 q^{68} + 8 q^{69} - 76 q^{71} + 16 q^{72} - 8 q^{73} + 24 q^{74} - 24 q^{75} + 80 q^{78} - 8 q^{79} - 8 q^{80} + 128 q^{81} + 48 q^{82} - 152 q^{84} - 152 q^{85} - 20 q^{88} + 64 q^{89} + 108 q^{90} + 8 q^{91} + 16 q^{92} + 128 q^{95} - 8 q^{97} - 40 q^{98} + 368 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1666, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)