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Properties

Label 1368.3.dx
Level $1368$
Weight $3$
Character orbit 1368.dx
Rep. character $\chi_{1368}(109,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1188$
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.dx (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
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 2928 1212 1716
Cusp forms 2832 1188 1644
Eisenstein series 96 24 72

Trace form

\( 1188 q + 6 q^{2} - 6 q^{7} + 9 q^{8} + O(q^{10}) \) \( 1188 q + 6 q^{2} - 6 q^{7} + 9 q^{8} - 9 q^{10} + 39 q^{14} + 36 q^{16} + 12 q^{17} + 42 q^{20} - 18 q^{22} + 12 q^{23} - 12 q^{25} - 69 q^{26} - 120 q^{28} - 18 q^{31} - 39 q^{32} + 72 q^{34} - 30 q^{38} + 60 q^{40} - 60 q^{41} + 363 q^{44} - 414 q^{46} + 300 q^{47} - 3912 q^{49} - 342 q^{50} - 21 q^{52} - 162 q^{55} - 84 q^{58} - 312 q^{62} - 189 q^{64} + 18 q^{65} - 234 q^{68} + 249 q^{70} + 12 q^{71} + 228 q^{73} - 207 q^{74} - 78 q^{76} - 12 q^{79} + 3 q^{80} - 195 q^{82} + 480 q^{86} - 945 q^{88} + 12 q^{89} + 1104 q^{92} + 492 q^{95} - 12 q^{97} + 1365 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{3}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)