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Properties

Label 504.4.bt
Level $504$
Weight $4$
Character orbit 504.bt
Rep. character $\chi_{504}(11,\cdot)$
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.bt (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

\( 568 q - 2 q^{3} - 2 q^{4} + 4 q^{6} - 2 q^{9} + O(q^{10}) \) \( 568 q - 2 q^{3} - 2 q^{4} + 4 q^{6} - 2 q^{9} - 18 q^{10} - 6 q^{11} - 164 q^{12} - 78 q^{14} - 2 q^{16} - 4 q^{18} - 4 q^{19} - 6 q^{20} + 14 q^{22} - 224 q^{24} - 6698 q^{25} - 24 q^{26} - 8 q^{27} + 60 q^{28} + 585 q^{30} - 110 q^{33} - 10 q^{34} + 750 q^{35} + 742 q^{36} - 825 q^{38} + 126 q^{40} - 12 q^{41} - 686 q^{42} - 4 q^{43} - 1539 q^{44} - 18 q^{46} - 557 q^{48} - 2 q^{49} - 381 q^{50} + 590 q^{51} + 129 q^{52} + 305 q^{54} - 1032 q^{56} + 100 q^{57} - 15 q^{58} + 1849 q^{60} - 8 q^{64} + 598 q^{66} - 4 q^{67} - 2742 q^{68} - 429 q^{70} + 1996 q^{72} - 4 q^{73} - 2781 q^{74} + 606 q^{75} + 62 q^{76} - 2129 q^{78} - 3297 q^{80} - 1234 q^{81} - 10 q^{82} - 3672 q^{83} + 1573 q^{84} + 8325 q^{86} - 511 q^{88} + 1272 q^{89} + 4049 q^{90} - 1380 q^{91} - 3996 q^{92} - 66 q^{94} - 409 q^{96} - 4 q^{97} - 4515 q^{98} + 1450 q^{99} + O(q^{100}) \)

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.