Properties

Label 504.4.w
Level $504$
Weight $4$
Character orbit 504.w
Rep. character $\chi_{504}(205,\cdot)$
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.w (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

\( 568 q + q^{2} + q^{4} + 4 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 568 q + q^{2} + q^{4} + 4 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{9} + 14 q^{10} + 55 q^{12} + 65 q^{14} + 46 q^{15} + q^{16} - 4 q^{17} + 85 q^{18} + 126 q^{20} + 14 q^{22} - 4 q^{23} + 276 q^{24} - 13404 q^{25} - 10 q^{26} - 68 q^{28} + 666 q^{30} + 2 q^{31} - 719 q^{32} + 214 q^{33} + 6 q^{34} + 522 q^{36} - 614 q^{38} - 110 q^{39} + 248 q^{40} - 4 q^{41} + 855 q^{42} - 259 q^{44} - 18 q^{46} - 1878 q^{47} + 549 q^{48} - 2 q^{49} - 763 q^{50} - 258 q^{52} + 1520 q^{54} + 484 q^{55} - 2002 q^{56} - 116 q^{57} - 34 q^{58} + 1754 q^{60} + 812 q^{62} + 722 q^{63} - 8 q^{64} + 502 q^{65} + 325 q^{66} + 1824 q^{68} + 140 q^{70} - 16 q^{71} - 3555 q^{72} - 4 q^{73} - 2246 q^{74} - 66 q^{76} + 2617 q^{78} + 2 q^{79} + 1597 q^{80} - 618 q^{81} + 6 q^{82} + 1321 q^{84} - 26 q^{86} + 52 q^{87} + 1022 q^{88} - 428 q^{89} + 4315 q^{90} - 1152 q^{92} + 33 q^{94} + 502 q^{95} - 2176 q^{96} - 4 q^{97} - 647 q^{98} + O(q^{100}) \)

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

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