Properties

Label 1368.3.bd
Level $1368$
Weight $3$
Character orbit 1368.bd
Rep. character $\chi_{1368}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 456 \)
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 976 320 656
Cusp forms 944 320 624
Eisenstein series 32 0 32

Trace form

\( 320q + 4q^{4} + O(q^{10}) \) \( 320q + 4q^{4} - 60q^{10} - 28q^{16} + 64q^{19} - 800q^{25} - 12q^{34} - 2176q^{49} - 240q^{52} - 128q^{58} - 368q^{64} - 864q^{70} + 160q^{73} - 692q^{76} - 116q^{82} + O(q^{100}) \)

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

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