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Properties

Label 1368.3.bt
Level $1368$
Weight $3$
Character orbit 1368.bt
Rep. character $\chi_{1368}(635,\cdot)$
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.bt (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

\( 952 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 17 q^{6} - 2 q^{9} + O(q^{10}) \) \( 952 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 17 q^{6} - 2 q^{9} - 6 q^{10} - 12 q^{11} - 27 q^{12} - 3 q^{14} - 2 q^{16} - 12 q^{18} - 8 q^{19} - 69 q^{20} - 27 q^{22} - 29 q^{24} - 2298 q^{25} - 18 q^{28} - 221 q^{30} - 6 q^{32} - 60 q^{33} - 21 q^{34} + 150 q^{35} - 131 q^{36} + 75 q^{38} + 72 q^{40} + 66 q^{41} + 50 q^{42} - 4 q^{43} + 51 q^{44} - 399 q^{48} + 3160 q^{49} + 75 q^{50} - 6 q^{51} - 16 q^{54} + 18 q^{57} + 6 q^{58} - 6 q^{59} + 243 q^{60} + 12 q^{62} + 256 q^{64} - 101 q^{66} - 54 q^{68} + 144 q^{70} - 237 q^{72} - 4 q^{73} + 204 q^{75} + 61 q^{76} - 354 q^{78} - 210 q^{80} - 114 q^{81} - 10 q^{82} - 12 q^{83} + 288 q^{84} - 330 q^{86} + 9 q^{90} - 306 q^{91} + 24 q^{94} - 163 q^{96} - 654 q^{98} - 454 q^{99} + O(q^{100}) \)

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.