Properties

Label 1344.4.cx
Level $1344$
Weight $4$
Character orbit 1344.cx
Rep. character $\chi_{1344}(11,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $12224$
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.cx (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1344 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1344, [\chi])\).

Total New Old
Modular forms 12352 12352 0
Cusp forms 12224 12224 0
Eisenstein series 128 128 0

Trace form

\( 12224q - 8q^{3} - 16q^{4} - 32q^{6} - 32q^{7} - 8q^{9} + O(q^{10}) \) \( 12224q - 8q^{3} - 16q^{4} - 32q^{6} - 32q^{7} - 8q^{9} - 16q^{10} - 8q^{12} - 64q^{13} - 32q^{15} - 16q^{16} - 8q^{18} - 16q^{19} - 16q^{21} - 64q^{22} + 1992q^{24} - 16q^{25} - 32q^{27} - 32q^{28} - 2328q^{30} - 32q^{31} - 64q^{34} + 1728q^{36} - 16q^{37} - 8q^{39} - 16q^{40} + 3144q^{42} - 64q^{43} - 8q^{45} - 16q^{46} - 32q^{48} - 32q^{49} - 8q^{51} + 3296q^{52} - 8q^{54} - 64q^{55} - 32q^{57} - 16q^{58} - 8q^{60} - 16q^{61} + 12032q^{64} + 120q^{66} - 6544q^{67} - 32q^{69} - 32q^{70} - 8q^{72} - 16q^{73} - 8q^{75} - 64q^{76} - 32q^{78} - 16q^{79} - 8q^{81} + 6944q^{82} - 4160q^{84} - 64q^{85} - 8q^{87} - 16q^{88} + 18688q^{90} - 32q^{91} + 424q^{93} - 16q^{94} - 12928q^{96} - 32q^{99} + O(q^{100}) \)

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

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