Properties

Label 1344.4.ch
Level $1344$
Weight $4$
Character orbit 1344.ch
Rep. character $\chi_{1344}(139,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $3072$
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.ch (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1024\)

Dimensions

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

Total New Old
Modular forms 6176 3072 3104
Cusp forms 6112 3072 3040
Eisenstein series 64 0 64

Trace form

\( 3072q + O(q^{10}) \) \( 3072q + 944q^{22} + 1520q^{28} + 2000q^{44} - 11424q^{50} - 4896q^{60} + 12096q^{64} + 1632q^{67} - 1792q^{71} + 5264q^{74} - 14112q^{78} + O(q^{100}) \)

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

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