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Properties

Label 624.4.cx
Level $624$
Weight $4$
Character orbit 624.cx
Rep. character $\chi_{624}(179,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1328$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.cx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(624, [\chi])\).

Total New Old
Modular forms 1360 1360 0
Cusp forms 1328 1328 0
Eisenstein series 32 32 0

Trace form

\( 1328 q - 2 q^{3} - 4 q^{4} - 96 q^{6} - 24 q^{7} + O(q^{10}) \) \( 1328 q - 2 q^{3} - 4 q^{4} - 96 q^{6} - 24 q^{7} - 4 q^{10} - 164 q^{12} - 8 q^{13} - 4 q^{16} - 12 q^{19} + 32 q^{22} - 1110 q^{24} - 272 q^{27} + 96 q^{28} - 34 q^{30} - 12 q^{33} - 768 q^{36} - 12 q^{37} - 1208 q^{39} - 1576 q^{40} - 1206 q^{42} - 436 q^{43} + 744 q^{45} - 12 q^{46} - 1204 q^{48} + 30176 q^{49} - 116 q^{51} - 44 q^{52} - 6 q^{54} - 296 q^{55} - 12 q^{58} - 4 q^{61} + 1064 q^{64} - 8768 q^{66} - 12 q^{67} - 110 q^{69} + 3066 q^{72} + 302 q^{75} + 2148 q^{76} - 5328 q^{78} - 4 q^{81} + 3148 q^{82} - 2064 q^{84} - 1512 q^{85} - 4 q^{87} + 4088 q^{88} - 6460 q^{90} - 3180 q^{91} - 168 q^{93} + 2368 q^{94} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

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