↑

Properties

Label 800.3.bc
Level $800$
Weight $3$
Character orbit 800.bc
Rep. character $\chi_{800}(157,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $568$
Sturm bound $360$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 800.bc (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(800, [\chi])\).

Total New Old
Modular forms 984 584 400
Cusp forms 936 568 368
Eisenstein series 48 16 32

Trace form

\( 568 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 8 q^{7} + 16 q^{8} + O(q^{10}) \) \( 568 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 8 q^{7} + 16 q^{8} - 8 q^{11} - 44 q^{12} + 4 q^{13} - 32 q^{14} - 8 q^{16} - 12 q^{18} - 128 q^{19} - 8 q^{21} + 116 q^{22} + 8 q^{23} + 64 q^{24} - 8 q^{26} + 40 q^{27} + 68 q^{28} - 16 q^{31} - 136 q^{32} + 8 q^{33} - 176 q^{34} - 8 q^{36} + 4 q^{37} - 276 q^{38} - 8 q^{41} + 28 q^{42} - 124 q^{43} + 352 q^{44} - 8 q^{46} - 232 q^{48} + 3640 q^{49} + 376 q^{51} + 104 q^{52} + 4 q^{53} - 112 q^{54} - 176 q^{56} + 8 q^{57} + 356 q^{58} - 136 q^{61} - 232 q^{62} + 8 q^{63} + 216 q^{64} + 536 q^{66} + 292 q^{67} + 376 q^{68} - 72 q^{69} - 520 q^{71} + 680 q^{72} + 8 q^{73} - 648 q^{76} + 200 q^{77} - 336 q^{78} + 388 q^{82} + 164 q^{83} - 392 q^{84} - 456 q^{86} - 456 q^{88} - 8 q^{91} - 172 q^{92} + 40 q^{93} - 576 q^{94} - 1096 q^{96} + 8 q^{97} + 472 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(800, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)