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Properties

Label 1368.2.db
Level $1368$
Weight $2$
Character orbit 1368.db
Rep. character $\chi_{1368}(11,\cdot)$
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.db (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

\( 472 q - 3 q^{2} - 2 q^{3} + q^{4} - 5 q^{6} - 2 q^{9} + O(q^{10}) \) \( 472 q - 3 q^{2} - 2 q^{3} + q^{4} - 5 q^{6} - 2 q^{9} - 6 q^{10} - 12 q^{11} - 7 q^{12} + q^{16} + 12 q^{18} - 8 q^{19} - 27 q^{20} - 10 q^{22} + 24 q^{24} + 436 q^{25} - 8 q^{27} - 6 q^{28} + 25 q^{30} - 3 q^{32} - 22 q^{33} - 22 q^{34} - 30 q^{35} + q^{36} - 3 q^{38} + 12 q^{40} + 33 q^{42} + 2 q^{43} + 45 q^{44} - 24 q^{46} + 20 q^{48} + 208 q^{49} - 21 q^{50} - 14 q^{51} - 15 q^{52} + q^{54} - 48 q^{56} + 10 q^{57} - 6 q^{58} - 6 q^{60} + 6 q^{62} - 32 q^{64} - 12 q^{65} - 39 q^{66} + 2 q^{67} - 18 q^{68} - 36 q^{70} - 29 q^{72} - 4 q^{73} - 60 q^{74} + 88 q^{75} + 19 q^{76} + 70 q^{78} - 6 q^{80} - 6 q^{81} + 2 q^{82} - 12 q^{83} + 18 q^{84} - 57 q^{86} + 14 q^{88} - 16 q^{90} - 18 q^{91} - 63 q^{92} - 6 q^{94} - 11 q^{96} + 2 q^{97} - 96 q^{98} - 48 q^{99} + O(q^{100}) \)

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.