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Properties

Label 672.4.ch
Level $672$
Weight $4$
Character orbit 672.ch
Rep. character $\chi_{672}(11,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $3040$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 672.ch (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 672 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(672, [\chi])\).

Total New Old
Modular forms 3104 3104 0
Cusp forms 3040 3040 0
Eisenstein series 64 64 0

Trace form

\( 3040 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} + O(q^{10}) \) \( 3040 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} - 488 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 1004 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} + 1188 q^{30} - 8 q^{33} + 96 q^{34} - 896 q^{36} - 8 q^{37} - 4 q^{39} - 584 q^{40} - 908 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 212 q^{51} + 1648 q^{52} + 436 q^{54} - 32 q^{55} - 16 q^{57} + 2008 q^{58} - 260 q^{60} - 8 q^{61} + 6016 q^{64} - 68 q^{66} + 3256 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 496 q^{75} - 32 q^{76} - 11720 q^{78} - 16 q^{79} - 3488 q^{82} - 2420 q^{84} + 1968 q^{85} - 4 q^{87} - 8 q^{88} - 9376 q^{90} + 3584 q^{91} - 220 q^{93} - 4816 q^{94} + 6456 q^{96} - 64 q^{97} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

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