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Properties

Label 1368.3.en
Level $1368$
Weight $3$
Character orbit 1368.en
Rep. character $\chi_{1368}(283,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2856$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1368.en (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1368 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1368, [\chi])\).

Total New Old
Modular forms 2904 2904 0
Cusp forms 2856 2856 0
Eisenstein series 48 48 0

Trace form

\( 2856 q - 3 q^{2} - 12 q^{3} - 3 q^{4} - 6 q^{6} - 6 q^{8} - 12 q^{9} + O(q^{10}) \) \( 2856 q - 3 q^{2} - 12 q^{3} - 3 q^{4} - 6 q^{6} - 6 q^{8} - 12 q^{9} - 12 q^{10} - 12 q^{11} - 3 q^{12} - 27 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{18} - 24 q^{19} - 6 q^{20} - 51 q^{22} - 84 q^{24} - 6 q^{25} - 78 q^{26} - 6 q^{27} + 36 q^{28} + 411 q^{30} - 3 q^{32} - 120 q^{33} - 39 q^{34} + 126 q^{35} + 54 q^{36} - 3 q^{38} - 153 q^{40} + 138 q^{41} - 231 q^{42} - 6 q^{43} + 39 q^{44} - 6 q^{46} + 60 q^{48} + 9498 q^{49} - 6 q^{50} - 12 q^{51} - 3 q^{52} + 201 q^{54} - 153 q^{56} - 12 q^{57} - 6 q^{58} - 6 q^{59} - 375 q^{60} - 204 q^{64} - 12 q^{65} - 882 q^{66} - 6 q^{67} + 3 q^{68} - 297 q^{70} + 228 q^{72} - 24 q^{73} - 747 q^{74} - 696 q^{75} - 3 q^{76} - 771 q^{78} - 12 q^{80} + 324 q^{81} - 12 q^{82} + 6 q^{83} - 297 q^{84} + 159 q^{86} - 381 q^{88} - 24 q^{89} - 363 q^{90} + 270 q^{91} - 759 q^{92} - 6 q^{94} + 345 q^{96} - 6 q^{97} - 867 q^{98} - 984 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

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