↑

Properties

Label 800.4.bb
Level $800$
Weight $4$
Character orbit 800.bb
Rep. character $\chi_{800}(107,\cdot)$
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.bb (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

\( 856 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 8 q^{7} + 88 q^{8} + O(q^{10}) \) \( 856 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 8 q^{7} + 88 q^{8} - 8 q^{11} - 44 q^{12} + 4 q^{13} - 64 q^{14} - 8 q^{16} + 36 q^{18} - 96 q^{19} - 8 q^{21} + 436 q^{22} + 8 q^{23} + 1472 q^{24} - 8 q^{26} - 104 q^{27} + 260 q^{28} - 336 q^{32} + 8 q^{33} + 1392 q^{34} - 8 q^{36} + 4 q^{37} + 2244 q^{38} - 8 q^{41} - 452 q^{42} + 868 q^{43} + 2464 q^{44} - 8 q^{46} + 8 q^{47} - 1384 q^{48} + 39592 q^{49} - 2984 q^{51} - 320 q^{52} + 4 q^{53} + 5936 q^{54} - 176 q^{56} + 2020 q^{58} - 3656 q^{61} - 496 q^{62} + 2744 q^{63} - 408 q^{64} - 1128 q^{66} + 1852 q^{67} - 1224 q^{68} - 216 q^{69} + 440 q^{71} - 664 q^{72} - 1672 q^{76} + 1376 q^{77} + 5744 q^{78} - 524 q^{82} + 2684 q^{83} - 2744 q^{84} + 2360 q^{86} - 5256 q^{88} - 8 q^{91} + 3796 q^{92} - 104 q^{93} + 832 q^{94} - 12360 q^{96} + 8 q^{97} - 2760 q^{98} + O(q^{100}) \)

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

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