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Properties

Label 2268.2.bt
Level $2268$
Weight $2$
Character orbit 2268.bt
Rep. character $\chi_{2268}(451,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $840$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.bt (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 756 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2268, [\chi])\).

Total New Old
Modular forms 2664 888 1776
Cusp forms 2520 840 1680
Eisenstein series 144 48 96

Trace form

\( 840 q + 3 q^{2} - 3 q^{4} + 18 q^{5} + 6 q^{8} + O(q^{10}) \) \( 840 q + 3 q^{2} - 3 q^{4} + 18 q^{5} + 6 q^{8} + 21 q^{14} - 3 q^{16} - 12 q^{22} - 6 q^{25} + 18 q^{26} - 12 q^{28} + 36 q^{29} - 27 q^{32} + 18 q^{34} + 6 q^{37} + 99 q^{38} + 36 q^{40} - 3 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{50} - 9 q^{52} + 12 q^{53} - 15 q^{56} - 3 q^{58} - 18 q^{61} + 99 q^{62} - 6 q^{64} - 18 q^{65} + 54 q^{68} - 36 q^{70} - 18 q^{73} - 93 q^{74} - 36 q^{76} + 36 q^{77} + 18 q^{80} - 18 q^{82} + 6 q^{85} - 135 q^{86} - 51 q^{88} - 48 q^{92} - 9 q^{94} + 117 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2268, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)