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Properties

Label 1368.2.bl
Level $1368$
Weight $2$
Character orbit 1368.bl
Rep. character $\chi_{1368}(293,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $472$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1368 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472 q - 6 q^{2} - 2 q^{4} + 7 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 472 q - 6 q^{2} - 2 q^{4} + 7 q^{6} - 4 q^{7} - 2 q^{9} - 6 q^{10} + 9 q^{12} - 3 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{18} + 15 q^{20} + 9 q^{22} + 11 q^{24} - 218 q^{25} + 2 q^{28} - 3 q^{30} - 6 q^{32} + 12 q^{33} + 15 q^{34} - 19 q^{36} + 33 q^{38} - 14 q^{39} + 12 q^{40} - 18 q^{41} + 4 q^{42} - 21 q^{44} - 6 q^{47} - 15 q^{48} - 216 q^{49} + 15 q^{50} + 4 q^{54} + 6 q^{55} + 6 q^{57} + 2 q^{58} + 27 q^{60} - 6 q^{62} + 26 q^{63} - 32 q^{64} + 27 q^{66} - 18 q^{68} - 24 q^{70} - 69 q^{72} - 4 q^{73} + 9 q^{76} + 12 q^{78} + 54 q^{80} + 6 q^{81} - 6 q^{82} - 84 q^{84} - 114 q^{86} - 30 q^{87} + 3 q^{90} - 12 q^{94} - 6 q^{95} + 9 q^{96} - 18 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

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