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Properties

Label 1368.3.cr
Level $1368$
Weight $3$
Character orbit 1368.cr
Rep. character $\chi_{1368}(829,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $396$
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.cr (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
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 976 404 572
Cusp forms 944 396 548
Eisenstein series 32 8 24

Trace form

\( 396 q + 3 q^{2} - 3 q^{4} - 8 q^{7} + O(q^{10}) \) \( 396 q + 3 q^{2} - 3 q^{4} - 8 q^{7} - 30 q^{14} - 15 q^{16} + 2 q^{17} - 68 q^{20} + 9 q^{22} + 2 q^{23} + 948 q^{25} - 16 q^{26} - 14 q^{28} - 177 q^{32} + 54 q^{34} - 138 q^{38} + 120 q^{40} + 78 q^{41} - 155 q^{44} - 94 q^{47} + 2628 q^{49} + 12 q^{52} + 48 q^{55} + 80 q^{58} + 104 q^{62} - 378 q^{64} - 140 q^{68} + 282 q^{70} + 6 q^{71} - 82 q^{73} + 232 q^{74} - 45 q^{76} - 6 q^{79} - 50 q^{80} + 271 q^{82} + 222 q^{86} + 6 q^{89} + 92 q^{92} - 74 q^{95} - 6 q^{97} + 129 q^{98} + O(q^{100}) \)

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

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