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Properties

Label 1368.2.ct
Level $1368$
Weight $2$
Character orbit 1368.ct
Rep. character $\chi_{1368}(1189,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $196$
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.ct (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
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 496 204 292
Cusp forms 464 196 268
Eisenstein series 32 8 24

Trace form

\( 196 q + q^{2} - 3 q^{4} - 8 q^{7} + 10 q^{8} + O(q^{10}) \) \( 196 q + q^{2} - 3 q^{4} - 8 q^{7} + 10 q^{8} - 6 q^{10} + 6 q^{14} + q^{16} + 2 q^{17} + 12 q^{20} - 9 q^{22} + 2 q^{23} + 88 q^{25} + 24 q^{26} + 8 q^{28} - 16 q^{31} + 11 q^{32} - 2 q^{34} - 16 q^{38} - 2 q^{40} - 2 q^{41} + 35 q^{44} - 24 q^{46} + 14 q^{47} + 180 q^{49} - 6 q^{50} + 4 q^{52} + 8 q^{55} + 16 q^{56} - 40 q^{58} + 4 q^{62} + 30 q^{64} + 28 q^{65} + 36 q^{68} - 16 q^{70} + 30 q^{71} + 6 q^{73} + 18 q^{74} - 29 q^{76} + 2 q^{79} + 14 q^{80} - 25 q^{82} + 20 q^{86} + 10 q^{88} + 2 q^{89} + 20 q^{92} - 20 q^{94} + 66 q^{95} + 14 q^{97} - 31 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)