Properties

Label 1368.2.cm
Level $1368$
Weight $2$
Character orbit 1368.cm
Rep. character $\chi_{1368}(835,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $472$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.cm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1368 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472 q - 2 q^{4} - 8 q^{6} - 8 q^{9} + O(q^{10}) \) \( 472 q - 2 q^{4} - 8 q^{6} - 8 q^{9} - 4 q^{11} - 2 q^{16} - 16 q^{17} - 8 q^{19} - 4 q^{20} - 14 q^{24} + 216 q^{25} + 16 q^{26} - 24 q^{28} + 4 q^{30} - 56 q^{35} - 44 q^{36} - 23 q^{38} - 16 q^{42} - 4 q^{43} + 20 q^{44} + 208 q^{49} - 22 q^{54} + 12 q^{57} + 6 q^{58} - 88 q^{62} + 16 q^{64} + 34 q^{66} - 10 q^{68} - 16 q^{73} + 8 q^{74} - 11 q^{76} - 44 q^{80} - 16 q^{82} - 4 q^{83} - 94 q^{92} + 20 q^{96} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

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