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Properties

Label 504.4.bf
Level $504$
Weight $4$
Character orbit 504.bf
Rep. character $\chi_{504}(115,\cdot)$
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.bf (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

\( 568 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 24 q^{6} - 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 568 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 24 q^{6} - 8 q^{8} - 2 q^{9} - 6 q^{10} + 2 q^{11} - 168 q^{12} + 56 q^{14} - 2 q^{16} - 12 q^{17} + 2 q^{18} - 12 q^{19} + 384 q^{20} - 18 q^{22} - 84 q^{24} - 6698 q^{25} + 18 q^{26} + 60 q^{28} + 493 q^{30} - 522 q^{32} - 6 q^{33} - 24 q^{34} - 258 q^{35} - 658 q^{36} + 867 q^{38} + 372 q^{40} + 568 q^{42} - 4 q^{43} + 255 q^{44} + 14 q^{46} - 81 q^{48} - 2 q^{49} + 727 q^{50} - 810 q^{51} + 381 q^{52} + 2199 q^{54} + 2158 q^{56} - 116 q^{57} + 17 q^{58} - 1331 q^{60} - 8 q^{64} + 996 q^{65} + 1728 q^{66} - 4 q^{67} + 2352 q^{68} + 927 q^{70} - 2908 q^{72} - 12 q^{73} - 697 q^{74} - 6 q^{75} - 192 q^{76} + 1677 q^{78} + 4041 q^{80} - 1234 q^{81} - 30 q^{82} + 3660 q^{83} + 5959 q^{84} - 19 q^{86} + 513 q^{88} + 1260 q^{89} + 3909 q^{90} + 1364 q^{91} - 896 q^{92} - 3069 q^{96} - 4965 q^{98} - 1466 q^{99} + O(q^{100}) \)

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.