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Properties

Label 1666.2.bl
Level $1666$
Weight $2$
Character orbit 1666.bl
Rep. character $\chi_{1666}(9,\cdot)$
Character field $\Q(\zeta_{168})$
Dimension $4032$
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.bl (of order \(168\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{168})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 12288 4032 8256
Cusp forms 11904 4032 7872
Eisenstein series 384 0 384

Trace form

\( 4032 q + 8 q^{5} + O(q^{10}) \) \( 4032 q + 8 q^{5} - 64 q^{11} + 8 q^{14} + 48 q^{15} - 336 q^{16} + 8 q^{17} - 16 q^{18} + 16 q^{22} + 192 q^{23} - 8 q^{25} - 48 q^{27} + 16 q^{28} + 48 q^{33} + 16 q^{35} - 16 q^{37} - 112 q^{41} - 240 q^{42} + 24 q^{45} + 336 q^{49} - 32 q^{50} - 16 q^{52} + 24 q^{54} - 208 q^{58} - 208 q^{59} + 24 q^{60} + 48 q^{62} - 48 q^{63} + 16 q^{67} + 48 q^{69} - 32 q^{70} + 32 q^{71} - 40 q^{73} - 304 q^{75} + 48 q^{77} - 160 q^{78} + 32 q^{79} - 8 q^{80} + 136 q^{83} + 32 q^{84} + 16 q^{85} + 24 q^{87} + 120 q^{90} + 16 q^{92} + 448 q^{93} - 32 q^{94} - 408 q^{95} + 192 q^{97} + 848 q^{99} + O(q^{100}) \)

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

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