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Properties

Label 1666.2.z
Level $1666$
Weight $2$
Character orbit 1666.z
Rep. character $\chi_{1666}(135,\cdot)$
Character field $\Q(\zeta_{42})$
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.z (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{42})\)
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

\( 1008 q + 84 q^{4} - 84 q^{9} + O(q^{10}) \) \( 1008 q + 84 q^{4} - 84 q^{9} - 8 q^{13} + 24 q^{15} + 84 q^{16} + 14 q^{17} - 4 q^{18} + 24 q^{19} + 40 q^{21} - 88 q^{25} - 8 q^{26} + 12 q^{30} + 28 q^{33} + 8 q^{34} - 28 q^{35} + 168 q^{36} - 44 q^{38} + 140 q^{42} - 48 q^{43} + 152 q^{47} + 220 q^{49} + 8 q^{50} - 92 q^{51} + 4 q^{52} - 44 q^{53} - 160 q^{55} + 88 q^{59} - 12 q^{60} - 168 q^{64} - 24 q^{66} + 12 q^{67} - 156 q^{69} - 4 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{77} + 136 q^{81} + 72 q^{83} - 92 q^{84} + 8 q^{85} + 96 q^{89} - 520 q^{93} - 28 q^{94} + 12 q^{98} + O(q^{100}) \)

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

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