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Properties

Label 1344.4.cz
Level $1344$
Weight $4$
Character orbit 1344.cz
Rep. character $\chi_{1344}(37,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $6144$
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.cz (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(1024\)

Dimensions

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

Total New Old
Modular forms 12352 6144 6208
Cusp forms 12224 6144 6080
Eisenstein series 128 0 128

Trace form

\( 6144 q + O(q^{10}) \) \( 6144 q - 1888 q^{22} - 1520 q^{28} + 1760 q^{38} + 2000 q^{44} - 11424 q^{50} + 3312 q^{52} + 5504 q^{59} + 4896 q^{60} + 12096 q^{64} - 5472 q^{66} - 1632 q^{67} - 1792 q^{71} - 5264 q^{74} - 14112 q^{78} + 10032 q^{80} - 6960 q^{82} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)