↑

Properties

Label 500.4.r
Level $500$
Weight $4$
Character orbit 500.r
Rep. character $\chi_{500}(3,\cdot)$
Character field $\Q(\zeta_{100})$
Dimension $8920$
Sturm bound $300$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 500 = 2^{2} \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 500.r (of order \(100\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 500 \)
Character field: \(\Q(\zeta_{100})\)
Sturm bound: \(300\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(500, [\chi])\).

Total New Old
Modular forms 9080 9080 0
Cusp forms 8920 8920 0
Eisenstein series 160 160 0

Trace form

\( 8920 q - 40 q^{2} - 40 q^{4} - 80 q^{5} - 40 q^{6} - 40 q^{8} - 80 q^{9} + O(q^{10}) \) \( 8920 q - 40 q^{2} - 40 q^{4} - 80 q^{5} - 40 q^{6} - 40 q^{8} - 80 q^{9} - 40 q^{10} - 40 q^{12} - 80 q^{13} - 40 q^{14} - 40 q^{16} - 80 q^{17} - 40 q^{18} - 40 q^{20} - 80 q^{21} - 40 q^{22} - 50 q^{24} - 80 q^{25} - 30 q^{26} - 40 q^{28} - 80 q^{29} - 40 q^{30} - 40 q^{32} - 80 q^{33} - 40 q^{34} - 40 q^{36} - 80 q^{37} - 2530 q^{38} - 2090 q^{40} - 80 q^{41} - 740 q^{42} + 1290 q^{44} - 80 q^{45} - 40 q^{46} + 6070 q^{48} - 100 q^{49} + 4370 q^{50} + 3830 q^{52} - 80 q^{53} + 3730 q^{54} - 40 q^{56} - 80 q^{57} - 1650 q^{58} - 6140 q^{60} - 80 q^{61} - 5390 q^{62} - 4870 q^{64} - 80 q^{65} - 40 q^{66} - 40 q^{68} - 80 q^{69} - 40 q^{70} + 230 q^{72} - 80 q^{73} - 50 q^{74} - 30 q^{76} - 80 q^{77} - 310 q^{78} - 40 q^{80} - 80 q^{81} + 8240 q^{82} + 11240 q^{84} - 5630 q^{85} - 40 q^{86} + 3920 q^{88} - 1510 q^{89} - 1390 q^{90} - 4340 q^{92} + 4480 q^{93} - 11080 q^{94} - 40 q^{96} + 18520 q^{97} - 13700 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(500, [\chi])\) into newform subspaces

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