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Properties

Label 1666.2.v
Level $1666$
Weight $2$
Character orbit 1666.v
Rep. character $\chi_{1666}(263,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $480$
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.v (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 2144 480 1664
Cusp forms 1888 480 1408
Eisenstein series 256 0 256

Trace form

\( 480 q + 8 q^{5} + O(q^{10}) \) \( 480 q + 8 q^{5} - 8 q^{11} + 112 q^{15} + 240 q^{16} + 8 q^{17} - 16 q^{18} + 16 q^{22} + 24 q^{23} - 8 q^{25} - 48 q^{27} + 48 q^{33} - 48 q^{37} + 32 q^{39} + 112 q^{41} + 64 q^{43} + 32 q^{44} + 24 q^{45} - 32 q^{50} + 32 q^{51} - 16 q^{52} + 112 q^{53} + 24 q^{54} + 48 q^{58} + 16 q^{59} + 56 q^{60} + 48 q^{62} - 32 q^{65} + 16 q^{67} + 160 q^{69} + 160 q^{71} - 40 q^{73} - 48 q^{74} - 136 q^{75} + 192 q^{78} - 8 q^{80} - 32 q^{83} - 48 q^{85} + 24 q^{87} + 32 q^{88} - 48 q^{90} + 16 q^{92} + 88 q^{93} - 32 q^{94} + 104 q^{95} + 192 q^{97} + 144 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)