Properties

Label 1666.2.bg
Level $1666$
Weight $2$
Character orbit 1666.bg
Rep. character $\chi_{1666}(81,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $2016$
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.bg (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 6144 2016 4128
Cusp forms 5952 2016 3936
Eisenstein series 192 0 192

Trace form

\( 2016 q - 168 q^{4} - 4 q^{5} - 4 q^{7} + O(q^{10}) \) \( 2016 q - 168 q^{4} - 4 q^{5} - 4 q^{7} - 32 q^{11} + 16 q^{13} + 4 q^{14} + 168 q^{16} - 4 q^{17} - 8 q^{18} + 20 q^{20} + 16 q^{21} + 8 q^{22} - 92 q^{23} + 132 q^{27} - 8 q^{28} - 24 q^{29} + 8 q^{31} - 40 q^{33} - 16 q^{34} + 48 q^{35} - 8 q^{37} - 16 q^{38} + 12 q^{39} + 104 q^{41} + 4 q^{44} - 272 q^{45} - 104 q^{47} + 16 q^{50} + 8 q^{52} - 12 q^{54} + 80 q^{55} - 4 q^{56} + 60 q^{57} + 104 q^{58} - 40 q^{61} - 16 q^{62} + 36 q^{63} + 336 q^{64} + 28 q^{65} - 8 q^{67} + 4 q^{68} - 104 q^{69} + 76 q^{71} + 8 q^{72} - 4 q^{73} + 12 q^{74} + 36 q^{75} - 80 q^{78} - 4 q^{79} - 4 q^{80} - 272 q^{81} + 128 q^{84} + 152 q^{85} + 32 q^{88} - 40 q^{89} - 108 q^{90} + 40 q^{91} - 16 q^{92} + 232 q^{95} - 136 q^{97} + 40 q^{98} - 368 q^{99} + O(q^{100}) \)

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

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