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Properties

Label 2166.2.h
Level $2166$
Weight $2$
Character orbit 2166.h
Rep. character $\chi_{2166}(293,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $224$
Sturm bound $760$

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Defining parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2166.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2166, [\chi])\).

Total New Old
Modular forms 840 224 616
Cusp forms 680 224 456
Eisenstein series 160 0 160

Trace form

\( 224 q + 3 q^{3} - 112 q^{4} + q^{6} - 12 q^{7} - q^{9} + O(q^{10}) \) \( 224 q + 3 q^{3} - 112 q^{4} + q^{6} - 12 q^{7} - q^{9} + 18 q^{13} - 6 q^{15} - 112 q^{16} + 6 q^{22} + q^{24} + 104 q^{25} + 6 q^{28} - 4 q^{30} + 3 q^{33} - 12 q^{34} - q^{36} + 60 q^{39} - 28 q^{42} + 14 q^{43} + 52 q^{45} - 3 q^{48} + 284 q^{49} - 72 q^{51} - 18 q^{52} - 26 q^{54} + 20 q^{55} - 8 q^{58} + 6 q^{60} + 22 q^{61} + 22 q^{63} + 224 q^{64} - 25 q^{66} - 36 q^{67} + 12 q^{70} - 3 q^{72} - 20 q^{73} - 6 q^{78} + 30 q^{79} + 15 q^{81} + 2 q^{82} - 24 q^{85} + 8 q^{87} + 78 q^{90} + 6 q^{91} - 2 q^{93} - 2 q^{96} - 18 q^{97} - 23 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2166, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2166, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2166, [\chi]) \cong \)