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Properties

Label 504.4.cz
Level $504$
Weight $4$
Character orbit 504.cz
Rep. character $\chi_{504}(187,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $568$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 504.cz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(504, [\chi])\).

Total New Old
Modular forms 584 584 0
Cusp forms 568 568 0
Eisenstein series 16 16 0

Trace form

\( 568 q + q^{2} - 6 q^{3} + q^{4} + 24 q^{6} - 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 568 q + q^{2} - 6 q^{3} + q^{4} + 24 q^{6} - 8 q^{8} - 2 q^{9} - 6 q^{10} - 4 q^{11} - 3 q^{12} - 67 q^{14} + q^{16} - 12 q^{17} - 55 q^{18} - 12 q^{19} - 384 q^{20} - 18 q^{22} - 84 q^{24} + 13396 q^{25} + 18 q^{26} + 60 q^{28} - 776 q^{30} + 261 q^{32} - 6 q^{33} + 24 q^{34} - 258 q^{35} - 658 q^{36} - 47 q^{42} - 4 q^{43} + 255 q^{44} + 14 q^{46} + 81 q^{48} - 2 q^{49} + 727 q^{50} + 1290 q^{51} + 3948 q^{54} - 1316 q^{56} - 116 q^{57} - 34 q^{58} - 6 q^{59} - 722 q^{60} - 8 q^{64} - 498 q^{65} - 651 q^{66} + 2 q^{67} - 828 q^{70} - 1615 q^{72} - 12 q^{73} + 1394 q^{74} - 756 q^{75} + 192 q^{76} + 1677 q^{78} + 4041 q^{80} + 614 q^{81} - 30 q^{82} - 3660 q^{83} + 2167 q^{84} + 38 q^{86} - 1026 q^{88} + 1260 q^{89} - 3909 q^{90} + 1364 q^{91} - 896 q^{92} - 3 q^{94} + 4842 q^{96} - 4965 q^{98} - 1466 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

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