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Properties

Label 1368.3.ch
Level $1368$
Weight $3$
Character orbit 1368.ch
Rep. character $\chi_{1368}(445,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $952$
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.ch (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1368 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 968 968 0
Cusp forms 952 952 0
Eisenstein series 16 16 0

Trace form

\( 952 q - 2 q^{4} - 17 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 952 q - 2 q^{4} - 17 q^{6} - 4 q^{7} - 2 q^{9} - 6 q^{10} + 27 q^{12} + 21 q^{14} - 6 q^{15} - 2 q^{16} - 4 q^{17} + 12 q^{18} + 51 q^{20} - 27 q^{22} - 4 q^{23} + 41 q^{24} + 2302 q^{25} + 32 q^{26} + 14 q^{28} - 135 q^{30} - 60 q^{33} - 21 q^{34} - 19 q^{36} - 287 q^{38} - 26 q^{39} - 78 q^{40} - 78 q^{41} + 184 q^{42} + 93 q^{44} + 2 q^{47} - 69 q^{48} - 3168 q^{49} - 51 q^{50} + 160 q^{54} - 54 q^{55} - 540 q^{56} + 54 q^{57} - 10 q^{58} + 243 q^{60} - 402 q^{62} + 194 q^{63} - 272 q^{64} - 300 q^{65} - 45 q^{66} + 14 q^{68} - 150 q^{70} - 12 q^{71} + 147 q^{72} - 4 q^{73} - 136 q^{74} - 63 q^{76} + 426 q^{78} - 72 q^{80} - 114 q^{81} + 6 q^{82} - 300 q^{84} + 198 q^{87} - 12 q^{89} - 15 q^{90} - 1234 q^{92} + 24 q^{94} - 102 q^{95} + 69 q^{96} + 648 q^{98} + O(q^{100}) \)

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.