Properties

Label 1344.4.bi
Level $1344$
Weight $4$
Character orbit 1344.bi
Rep. character $\chi_{1344}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $384$
Sturm bound $1024$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1344.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1344, [\chi])\).

Total New Old
Modular forms 1584 384 1200
Cusp forms 1488 384 1104
Eisenstein series 96 0 96

Trace form

\( 384q + O(q^{10}) \) \( 384q + 4800q^{25} - 720q^{49} + 1296q^{73} + 3696q^{81} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)