Properties

Label 1344.4.u
Level $1344$
Weight $4$
Character orbit 1344.u
Rep. character $\chi_{1344}(559,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 192 1376
Cusp forms 1504 192 1312
Eisenstein series 64 0 64

Trace form

\( 192q + O(q^{10}) \) \( 192q - 40q^{11} + 656q^{23} - 400q^{29} + 456q^{35} - 16q^{37} + 808q^{43} + 752q^{53} - 3288q^{67} - 896q^{71} - 15552q^{81} - 3496q^{91} + 360q^{99} + O(q^{100}) \)

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

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