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Properties

Label 1666.2.j
Level $1666$
Weight $2$
Character orbit 1666.j
Rep. character $\chi_{1666}(67,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 536 120 416
Cusp forms 472 120 352
Eisenstein series 64 0 64

Trace form

\( 120 q - 60 q^{4} + 44 q^{9} + O(q^{10}) \) \( 120 q - 60 q^{4} + 44 q^{9} - 8 q^{13} - 8 q^{15} - 60 q^{16} - 4 q^{18} - 4 q^{19} + 40 q^{25} - 8 q^{26} - 4 q^{30} + 28 q^{33} + 8 q^{34} - 88 q^{36} + 12 q^{38} - 80 q^{43} + 12 q^{47} - 40 q^{50} + 44 q^{51} + 4 q^{52} + 20 q^{53} + 120 q^{55} - 24 q^{59} + 4 q^{60} + 120 q^{64} - 24 q^{66} - 4 q^{67} - 128 q^{69} - 4 q^{72} + 8 q^{76} - 64 q^{81} + 16 q^{83} + 24 q^{85} + 16 q^{86} + 12 q^{89} + 28 q^{93} - 28 q^{94} + O(q^{100}) \)

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

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