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Properties

Label 1368.3.ea
Level $1368$
Weight $3$
Character orbit 1368.ea
Rep. character $\chi_{1368}(5,\cdot)$
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.ea (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

\( 2856 q - 9 q^{2} - 3 q^{4} - 6 q^{6} + 6 q^{7} - 12 q^{9} + O(q^{10}) \) \( 2856 q - 9 q^{2} - 3 q^{4} - 6 q^{6} + 6 q^{7} - 12 q^{9} - 12 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 3 q^{16} - 12 q^{18} - 18 q^{20} - 51 q^{22} - 18 q^{23} + 126 q^{24} - 6 q^{25} - 216 q^{26} - 60 q^{28} + 411 q^{30} - 12 q^{31} - 9 q^{32} - 120 q^{33} - 39 q^{34} + 54 q^{36} - 9 q^{38} - 24 q^{39} + 147 q^{40} - 18 q^{41} - 81 q^{42} + 153 q^{44} - 6 q^{46} - 18 q^{47} + 390 q^{48} - 9486 q^{49} - 3 q^{52} + 201 q^{54} - 174 q^{55} - 459 q^{56} - 12 q^{57} - 6 q^{58} - 675 q^{60} - 36 q^{62} + 282 q^{63} + 192 q^{64} + 438 q^{66} - 9 q^{68} + 291 q^{70} - 156 q^{72} - 24 q^{73} + 405 q^{74} - 3 q^{76} + 789 q^{78} - 6 q^{79} + 324 q^{81} - 12 q^{82} + 291 q^{84} + 477 q^{86} - 6 q^{87} - 381 q^{88} - 189 q^{90} - 9 q^{92} - 6 q^{94} - 18 q^{95} - 471 q^{96} - 6 q^{97} + 477 q^{98} + O(q^{100}) \)

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.