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Properties

Label 1666.2.u
Level $1666$
Weight $2$
Character orbit 1666.u
Rep. character $\chi_{1666}(137,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $912$
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.u (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 3072 912 2160
Cusp forms 2976 912 2064
Eisenstein series 96 0 96

Trace form

\( 912 q + 76 q^{4} - 4 q^{5} + 28 q^{6} + 4 q^{7} + 112 q^{9} + O(q^{10}) \) \( 912 q + 76 q^{4} - 4 q^{5} + 28 q^{6} + 4 q^{7} + 112 q^{9} + 4 q^{11} - 8 q^{13} + 4 q^{14} + 20 q^{15} + 76 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{19} + 8 q^{20} - 8 q^{21} + 20 q^{22} + 88 q^{25} + 36 q^{26} - 8 q^{28} + 20 q^{29} + 4 q^{30} - 8 q^{31} + 28 q^{33} + 8 q^{34} + 24 q^{35} - 140 q^{36} + 4 q^{38} - 44 q^{39} - 56 q^{40} - 8 q^{41} + 88 q^{42} + 16 q^{43} - 52 q^{44} + 220 q^{45} - 152 q^{46} + 8 q^{47} - 12 q^{49} - 40 q^{50} + 32 q^{52} + 112 q^{53} - 180 q^{54} + 156 q^{55} - 52 q^{56} - 40 q^{57} + 128 q^{58} + 36 q^{59} - 52 q^{60} + 24 q^{61} + 8 q^{62} + 48 q^{63} - 152 q^{64} + 28 q^{65} + 24 q^{66} + 4 q^{67} + 24 q^{68} + 108 q^{69} + 64 q^{70} - 56 q^{71} + 4 q^{72} + 48 q^{73} + 40 q^{74} + 52 q^{75} - 8 q^{76} + 48 q^{77} - 32 q^{78} + 12 q^{79} + 24 q^{80} + 116 q^{81} - 8 q^{83} + 16 q^{84} + 108 q^{86} - 220 q^{87} + 4 q^{88} + 56 q^{89} + 72 q^{90} + 52 q^{91} + 4 q^{93} + 136 q^{94} + 32 q^{95} + 4 q^{98} - 80 q^{99} + O(q^{100}) \)

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

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