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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

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

Display 100 coefficients 10 coefficients

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

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