Properties

Label 1344.4.cj
Level $1344$
Weight $4$
Character orbit 1344.cj
Rep. character $\chi_{1344}(125,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $6112$
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.cj (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1344 \)
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 6176 0
Cusp forms 6112 6112 0
Eisenstein series 64 64 0

Trace form

\( 6112q - 32q^{4} - 16q^{7} - 16q^{9} + O(q^{10}) \) \( 6112q - 32q^{4} - 16q^{7} - 16q^{9} - 16q^{15} - 32q^{16} - 16q^{18} - 8q^{21} - 32q^{22} - 32q^{25} - 16q^{28} - 2336q^{30} - 896q^{36} - 32q^{37} - 16q^{39} - 3168q^{42} - 32q^{43} - 32q^{46} - 16q^{49} - 16q^{51} - 16q^{57} - 32q^{58} - 16q^{60} - 16q^{63} + 12064q^{64} + 6496q^{67} - 16q^{70} - 16q^{72} - 16q^{78} - 32q^{79} - 16q^{81} - 4152q^{84} - 32q^{85} - 32q^{88} - 16q^{91} - 448q^{93} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.