Properties

Label 1344.4.w
Level $1344$
Weight $4$
Character orbit 1344.w
Rep. character $\chi_{1344}(337,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1024\)

Dimensions

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

Total New Old
Modular forms 1568 144 1424
Cusp forms 1504 144 1360
Eisenstein series 64 0 64

Trace form

\( 144q + O(q^{10}) \) \( 144q - 40q^{11} + 240q^{15} + 48q^{19} - 400q^{29} - 16q^{37} + 1672q^{43} - 7056q^{49} + 1488q^{51} - 752q^{53} + 1824q^{61} - 504q^{63} - 1952q^{65} - 408q^{67} + 1056q^{69} + 2208q^{75} - 1904q^{77} + 11984q^{79} - 11664q^{81} + 5360q^{83} + 480q^{85} - 360q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)