↑

Properties

Label 2166.2.r
Level $2166$
Weight $2$
Character orbit 2166.r
Rep. character $\chi_{2166}(65,\cdot)$
Character field $\Q(\zeta_{114})$
Dimension $4608$
Sturm bound $760$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2166.r (of order \(114\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1083 \)
Character field: \(\Q(\zeta_{114})\)
Sturm bound: \(760\)

Dimensions

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

Total New Old
Modular forms 13824 4608 9216
Cusp forms 13536 4608 8928
Eisenstein series 288 0 288

Trace form

\( 4608 q - 16 q^{3} + 128 q^{4} + q^{6} - 12 q^{7} - 20 q^{9} + O(q^{10}) \) \( 4608 q - 16 q^{3} + 128 q^{4} + q^{6} - 12 q^{7} - 20 q^{9} + 18 q^{13} - 6 q^{15} + 128 q^{16} + 18 q^{19} + 6 q^{22} + q^{24} - 136 q^{25} + 38 q^{27} + 6 q^{28} + 110 q^{30} + 3 q^{33} - 12 q^{34} - q^{36} + 112 q^{39} - 16 q^{42} - 360 q^{43} - 138 q^{45} - 3 q^{48} - 184 q^{49} - 72 q^{51} - 18 q^{52} - 14 q^{54} - 12 q^{55} - 48 q^{57} + 8 q^{58} + 6 q^{60} + 14 q^{61} - 180 q^{63} - 256 q^{64} - 25 q^{66} - 36 q^{67} - 292 q^{70} - 3 q^{72} + 4 q^{73} - 114 q^{75} - 12 q^{76} - 6 q^{78} + 30 q^{79} + 12 q^{81} - 66 q^{82} + 8 q^{85} + 206 q^{87} + 78 q^{90} + 6 q^{91} + 14 q^{93} - 2 q^{96} - 18 q^{97} - 23 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2166, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1083, [\chi])\)\(^{\oplus 2}\)