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Properties

Label 1666.2.k
Level $1666$
Weight $2$
Character orbit 1666.k
Rep. character $\chi_{1666}(239,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $432$
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.k (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 1536 432 1104
Cusp forms 1488 432 1056
Eisenstein series 48 0 48

Trace form

\( 432 q + 4 q^{3} - 72 q^{4} + 4 q^{5} - 16 q^{6} + 12 q^{7} - 84 q^{9} + O(q^{10}) \) \( 432 q + 4 q^{3} - 72 q^{4} + 4 q^{5} - 16 q^{6} + 12 q^{7} - 84 q^{9} + 12 q^{10} + 8 q^{11} + 4 q^{12} + 16 q^{13} + 8 q^{14} - 20 q^{15} - 72 q^{16} + 4 q^{17} + 8 q^{18} + 40 q^{19} + 4 q^{20} + 24 q^{21} - 20 q^{22} + 12 q^{24} - 48 q^{25} - 12 q^{26} + 16 q^{27} + 12 q^{28} - 20 q^{29} + 8 q^{30} + 40 q^{31} + 56 q^{33} + 4 q^{34} + 12 q^{35} - 84 q^{36} - 56 q^{37} + 8 q^{38} - 60 q^{39} - 16 q^{40} + 56 q^{41} - 88 q^{42} + 40 q^{43} - 20 q^{44} - 160 q^{45} - 52 q^{46} - 80 q^{47} - 24 q^{48} + 40 q^{49} + 40 q^{50} - 40 q^{52} - 112 q^{53} - 36 q^{54} - 132 q^{55} - 20 q^{56} + 96 q^{57} - 80 q^{58} + 36 q^{59} - 20 q^{60} - 104 q^{61} + 40 q^{62} - 96 q^{63} - 72 q^{64} + 56 q^{65} + 72 q^{66} + 64 q^{67} - 24 q^{68} + 36 q^{69} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 4 q^{73} - 4 q^{74} + 132 q^{75} + 40 q^{76} + 36 q^{77} + 32 q^{78} + 80 q^{79} - 24 q^{80} + 8 q^{81} + 24 q^{82} + 20 q^{83} + 24 q^{84} - 36 q^{86} + 4 q^{87} + 8 q^{88} - 116 q^{89} + 84 q^{90} - 80 q^{91} + 64 q^{93} - 76 q^{94} + 64 q^{95} + 12 q^{96} - 136 q^{97} + 20 q^{98} + 80 q^{99} + O(q^{100}) \)

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

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