Properties

Label 1344.4.y
Level $1344$
Weight $4$
Character orbit 1344.y
Rep. character $\chi_{1344}(209,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $376$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
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 392 1176
Cusp forms 1504 376 1128
Eisenstein series 64 16 48

Trace form

\( 376q + O(q^{10}) \) \( 376q + 8q^{15} - 56q^{21} - 8q^{37} + 8q^{43} - 8q^{49} - 1288q^{51} - 1368q^{63} + 1640q^{67} + 16q^{79} - 8q^{81} - 1008q^{85} + 3176q^{91} + 104q^{93} + 2920q^{99} + O(q^{100}) \)

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

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