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Properties

Label 2268.2.ci
Level $2268$
Weight $2$
Character orbit 2268.ci
Rep. character $\chi_{2268}(179,\cdot)$
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.ci (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

\( 840 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 18 q^{8} + O(q^{10}) \) \( 840 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 18 q^{8} + 3 q^{10} - 24 q^{13} - 24 q^{14} - 3 q^{16} + 18 q^{17} + 12 q^{20} - 12 q^{22} - 6 q^{25} - 12 q^{28} + 12 q^{29} + 63 q^{32} - 6 q^{34} - 12 q^{37} - 45 q^{38} - 33 q^{40} + 24 q^{41} - 6 q^{46} - 12 q^{49} + 27 q^{50} - 3 q^{52} + 27 q^{56} - 3 q^{58} - 6 q^{61} + 117 q^{62} - 6 q^{64} + 54 q^{65} + 12 q^{68} - 21 q^{70} - 12 q^{73} - 15 q^{74} - 12 q^{77} - 6 q^{82} + 6 q^{85} + 9 q^{86} - 27 q^{88} + 18 q^{89} - 48 q^{92} - 3 q^{94} - 24 q^{97} - 162 q^{98} + O(q^{100}) \)

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

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