Properties

Label 684.3.ba
Level $684$
Weight $3$
Character orbit 684.ba
Rep. character $\chi_{684}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).

Total New Old
Modular forms 496 160 336
Cusp forms 464 160 304
Eisenstein series 32 0 32

Trace form

\( 160q - 4q^{4} + O(q^{10}) \) \( 160q - 4q^{4} - 60q^{10} + 48q^{13} - 28q^{16} + 400q^{25} + 12q^{34} - 1216q^{49} - 240q^{52} + 128q^{58} + 16q^{61} + 464q^{64} - 144q^{70} + 240q^{73} - 236q^{76} - 284q^{82} + 352q^{85} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)