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Properties

Label 1368.3.u
Level $1368$
Weight $3$
Character orbit 1368.u
Rep. character $\chi_{1368}(373,\cdot)$
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.u (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

\( 952 q - 3 q^{2} + q^{4} + 7 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 952 q - 3 q^{2} + q^{4} + 7 q^{6} - 4 q^{7} - 2 q^{9} - 6 q^{10} - 27 q^{12} - 6 q^{15} + q^{16} - 4 q^{17} - 12 q^{18} + 51 q^{20} + 2 q^{23} - 88 q^{24} - 4604 q^{25} + 32 q^{26} + 14 q^{28} - 135 q^{30} - 3 q^{32} - 6 q^{33} - 91 q^{36} + 193 q^{38} - 26 q^{39} - 137 q^{42} + 93 q^{44} - 4 q^{47} + 162 q^{48} - 3168 q^{49} + 51 q^{50} - 3 q^{52} - 323 q^{54} - 54 q^{55} + 540 q^{56} - 66 q^{57} - 10 q^{58} + 72 q^{60} - 402 q^{62} - 100 q^{63} - 272 q^{64} + 300 q^{65} + 315 q^{66} + 14 q^{68} - 12 q^{71} + 147 q^{72} - 4 q^{73} + 68 q^{74} + 123 q^{76} + 24 q^{78} - 6 q^{79} - 72 q^{80} + 54 q^{81} + 6 q^{82} + 300 q^{84} + 159 q^{86} + 198 q^{87} - 12 q^{89} - 198 q^{90} + 617 q^{92} - 24 q^{94} + 48 q^{95} + 69 q^{96} - 6 q^{97} + 648 q^{98} + O(q^{100}) \)

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.