↑

Properties

Label 504.4.cq
Level $504$
Weight $4$
Character orbit 504.cq
Rep. character $\chi_{504}(277,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $568$
Sturm bound $384$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 504.cq (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

\( 568 q - 2 q^{2} - 2 q^{4} + 4 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 568 q - 2 q^{2} - 2 q^{4} + 4 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{9} + 14 q^{10} + 52 q^{12} - 58 q^{14} + 46 q^{15} - 2 q^{16} - 4 q^{17} - 68 q^{18} + 126 q^{20} + 14 q^{22} + 2 q^{23} + 276 q^{24} + 6702 q^{25} - 10 q^{26} - 68 q^{28} - 603 q^{30} - 4 q^{31} + 1438 q^{32} - 110 q^{33} + 6 q^{34} + 522 q^{36} + 307 q^{38} + 52 q^{39} - 124 q^{40} - 4 q^{41} + 1470 q^{42} - 259 q^{44} - 18 q^{46} + 3756 q^{47} + 549 q^{48} - 2 q^{49} - 763 q^{50} + 129 q^{52} - 511 q^{54} + 484 q^{55} + 1472 q^{56} - 116 q^{57} + 17 q^{58} - 739 q^{60} + 812 q^{62} - 1336 q^{63} - 8 q^{64} - 1004 q^{65} - 512 q^{66} - 912 q^{68} + 443 q^{70} - 16 q^{71} + 972 q^{72} - 4 q^{73} + 1123 q^{74} - 66 q^{76} + 2617 q^{78} - 4 q^{79} + 1597 q^{80} + 1230 q^{81} + 6 q^{82} - 4145 q^{84} + 13 q^{86} - 110 q^{87} - 511 q^{88} - 428 q^{89} + 4315 q^{90} - 1152 q^{92} - 66 q^{94} - 1004 q^{95} - 3793 q^{96} - 4 q^{97} - 647 q^{98} + O(q^{100}) \)

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.