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Properties

Label 1666.2.l
Level $1666$
Weight $2$
Character orbit 1666.l
Rep. character $\chi_{1666}(393,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $244$
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.l (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 1072 244 828
Cusp forms 944 244 700
Eisenstein series 128 0 128

Trace form

\( 244 q + 8 q^{5} - 4 q^{9} + O(q^{10}) \) \( 244 q + 8 q^{5} - 4 q^{9} - 8 q^{10} - 12 q^{11} + 4 q^{12} - 8 q^{15} - 244 q^{16} + 16 q^{17} - 28 q^{18} + 8 q^{19} - 8 q^{22} + 32 q^{23} + 4 q^{24} - 8 q^{26} + 36 q^{27} - 16 q^{33} - 16 q^{34} - 4 q^{36} - 8 q^{37} - 32 q^{39} + 44 q^{43} - 24 q^{44} + 56 q^{45} + 44 q^{50} - 16 q^{51} + 24 q^{52} - 104 q^{53} + 52 q^{54} + 8 q^{57} + 28 q^{59} + 8 q^{60} + 16 q^{61} - 48 q^{62} + 16 q^{65} - 12 q^{66} + 8 q^{67} + 32 q^{69} + 24 q^{71} - 80 q^{73} + 56 q^{74} + 36 q^{75} - 8 q^{76} + 88 q^{79} - 8 q^{80} + 20 q^{82} + 44 q^{83} - 56 q^{85} - 24 q^{86} - 88 q^{87} - 28 q^{88} + 48 q^{90} - 16 q^{92} + 72 q^{93} - 48 q^{94} + 16 q^{95} + 84 q^{97} + 144 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)