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Properties

Label 1666.2.r
Level $1666$
Weight $2$
Character orbit 1666.r
Rep. character $\chi_{1666}(169,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $504$
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.r (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 1536 504 1032
Cusp forms 1488 504 984
Eisenstein series 48 0 48

Trace form

\( 504 q - 84 q^{4} + 84 q^{9} + O(q^{10}) \) \( 504 q - 84 q^{4} + 84 q^{9} - 4 q^{13} - 24 q^{15} - 84 q^{16} - 2 q^{17} - 8 q^{18} - 24 q^{19} - 4 q^{21} + 76 q^{25} + 20 q^{26} + 24 q^{30} - 40 q^{33} - 8 q^{34} + 4 q^{35} + 84 q^{36} - 40 q^{38} - 32 q^{42} + 48 q^{43} - 32 q^{47} + 92 q^{49} - 8 q^{50} - 16 q^{51} - 4 q^{52} - 4 q^{53} - 140 q^{55} + 68 q^{59} - 24 q^{60} - 84 q^{64} + 24 q^{66} + 24 q^{67} + 12 q^{68} + 108 q^{69} + 4 q^{70} - 8 q^{72} + 4 q^{76} + 8 q^{77} - 64 q^{81} - 96 q^{83} + 80 q^{84} - 8 q^{85} - 72 q^{87} - 60 q^{89} + 52 q^{93} - 8 q^{94} + 60 q^{98} + O(q^{100}) \)

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

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