↑

Properties

Label 800.4.v
Level $800$
Weight $4$
Character orbit 800.v
Rep. character $\chi_{800}(43,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $856$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 800.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(800, [\chi])\).

Total New Old
Modular forms 1464 872 592
Cusp forms 1416 856 560
Eisenstein series 48 16 32

Trace form

\( 856 q + 4 q^{2} + 4 q^{3} - 8 q^{6} - 80 q^{8} + O(q^{10}) \) \( 856 q + 4 q^{2} + 4 q^{3} - 8 q^{6} - 80 q^{8} - 8 q^{11} - 44 q^{12} + 4 q^{13} + 64 q^{14} - 8 q^{16} - 28 q^{18} + 96 q^{19} - 8 q^{21} + 436 q^{22} - 1472 q^{24} - 8 q^{26} + 112 q^{27} - 252 q^{28} + 344 q^{32} + 8 q^{33} - 1392 q^{34} - 8 q^{36} + 4 q^{37} + 172 q^{38} - 8 q^{41} + 460 q^{42} - 860 q^{43} - 2464 q^{44} - 8 q^{46} + 8 q^{47} - 3496 q^{48} - 39592 q^{49} - 2984 q^{51} + 328 q^{52} + 4 q^{53} - 5936 q^{54} - 176 q^{56} + 8 q^{57} + 2020 q^{58} - 3656 q^{61} + 440 q^{62} - 2744 q^{63} + 408 q^{64} - 1128 q^{66} - 1844 q^{67} - 1224 q^{68} + 216 q^{69} + 440 q^{71} + 3432 q^{72} + 8 q^{73} - 1672 q^{76} - 1368 q^{77} + 5968 q^{78} - 588 q^{82} - 2676 q^{83} + 2744 q^{84} + 2360 q^{86} - 2568 q^{87} + 5880 q^{88} - 8 q^{91} + 3284 q^{92} - 104 q^{93} - 832 q^{94} - 12360 q^{96} + 8 q^{97} - 3480 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)