Properties

Label 1344.4.s
Level $1344$
Weight $4$
Character orbit 1344.s
Rep. character $\chi_{1344}(239,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 288 1280
Cusp forms 1504 288 1216
Eisenstein series 64 0 64

Trace form

\( 288q + O(q^{10}) \) \( 288q + 48q^{19} - 264q^{27} + 1200q^{39} - 864q^{43} + 14112q^{49} + 576q^{55} + 1824q^{61} - 1632q^{67} + 3304q^{75} - 480q^{85} + 2576q^{87} + 4272q^{93} + 5312q^{99} + O(q^{100}) \)

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

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