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Properties

Label 1666.2.o
Level $1666$
Weight $2$
Character orbit 1666.o
Rep. character $\chi_{1666}(361,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
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.o (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 1072 240 832
Cusp forms 944 240 704
Eisenstein series 128 0 128

Trace form

\( 240 q + 120 q^{4} - 4 q^{5} + O(q^{10}) \) \( 240 q + 120 q^{4} - 4 q^{5} - 20 q^{11} + 16 q^{13} - 120 q^{16} - 4 q^{17} - 8 q^{18} - 8 q^{20} + 40 q^{22} - 8 q^{23} + 48 q^{27} + 8 q^{29} + 8 q^{31} - 40 q^{33} - 16 q^{34} + 8 q^{37} - 16 q^{38} + 12 q^{39} - 8 q^{41} + 20 q^{44} + 8 q^{45} + 32 q^{46} + 8 q^{47} + 16 q^{50} + 32 q^{51} + 8 q^{52} - 12 q^{54} + 80 q^{55} + 72 q^{57} + 32 q^{58} - 40 q^{61} + 40 q^{62} - 240 q^{64} + 100 q^{65} - 40 q^{67} + 4 q^{68} - 48 q^{69} + 56 q^{71} + 8 q^{72} - 4 q^{73} - 28 q^{74} + 36 q^{75} - 36 q^{79} - 4 q^{80} + 192 q^{81} + 104 q^{85} - 64 q^{86} + 20 q^{88} - 40 q^{89} - 24 q^{90} - 16 q^{92} + 24 q^{95} - 136 q^{97} + 208 q^{99} + O(q^{100}) \)

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

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