Properties

Label 1344.4.ci
Level $1344$
Weight $4$
Character orbit 1344.ci
Rep. character $\chi_{1344}(155,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $4608$
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.ci (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
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 4608 1568
Cusp forms 6112 4608 1504
Eisenstein series 64 0 64

Trace form

\( 4608q + O(q^{10}) \) \( 4608q - 2320q^{30} - 880q^{36} + 1152q^{55} + 9504q^{58} - 6528q^{67} + 2016q^{70} - 20832q^{76} - 10128q^{78} + 11328q^{79} + 6240q^{88} + 17856q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)