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Properties

Label 1666.2.e
Level $1666$
Weight $2$
Character orbit 1666.e
Rep. character $\chi_{1666}(851,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $104$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 536 104 432
Cusp forms 472 104 368
Eisenstein series 64 0 64

Trace form

\( 104 q - 52 q^{4} - 4 q^{5} - 44 q^{9} + O(q^{10}) \) \( 104 q - 52 q^{4} - 4 q^{5} - 44 q^{9} + 4 q^{11} - 8 q^{13} + 24 q^{15} - 52 q^{16} - 4 q^{17} - 12 q^{18} + 4 q^{19} + 8 q^{20} - 8 q^{22} - 32 q^{23} - 56 q^{25} + 8 q^{26} + 24 q^{29} - 12 q^{30} - 8 q^{31} + 28 q^{33} + 8 q^{34} + 88 q^{36} + 56 q^{37} + 4 q^{38} + 52 q^{39} - 8 q^{41} - 64 q^{43} + 4 q^{44} - 32 q^{45} + 16 q^{46} - 20 q^{47} - 8 q^{50} + 4 q^{52} + 12 q^{53} - 12 q^{54} - 40 q^{55} - 120 q^{57} + 16 q^{58} + 8 q^{59} - 12 q^{60} + 24 q^{61} + 8 q^{62} + 104 q^{64} - 4 q^{65} + 24 q^{66} + 60 q^{67} - 4 q^{68} + 80 q^{69} - 56 q^{71} - 12 q^{72} - 36 q^{73} + 12 q^{74} + 52 q^{75} - 8 q^{76} + 52 q^{79} - 4 q^{80} + 48 q^{83} + 24 q^{86} - 24 q^{87} + 4 q^{88} + 28 q^{89} + 72 q^{90} + 64 q^{92} - 4 q^{93} - 4 q^{94} - 80 q^{95} - 56 q^{97} + 48 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)