↑

Properties

Label 800.6.ba
Level $800$
Weight $6$
Character orbit 800.ba
Rep. character $\chi_{800}(149,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1432$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.ba (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(800, [\chi])\).

Total New Old
Modular forms 2424 1448 976
Cusp forms 2376 1432 944
Eisenstein series 48 16 32

Trace form

\( 1432 q + 8 q^{4} - 8 q^{6} + 8 q^{9} + O(q^{10}) \) \( 1432 q + 8 q^{4} - 8 q^{6} + 8 q^{9} - 8 q^{11} + 4968 q^{14} - 8 q^{16} + 8 q^{19} - 8 q^{21} + 20888 q^{24} + 25952 q^{26} + 8 q^{29} + 46112 q^{31} - 248 q^{34} + 62312 q^{36} + 8 q^{39} - 8 q^{41} + 8 q^{44} - 8 q^{46} + 43696 q^{51} + 233288 q^{54} + 64672 q^{56} - 57912 q^{59} - 192328 q^{61} - 651376 q^{64} + 289496 q^{66} - 89272 q^{69} - 287688 q^{71} - 210360 q^{74} - 512008 q^{76} + 775136 q^{84} + 182072 q^{86} + 8 q^{89} - 8 q^{91} + 770656 q^{94} - 1005048 q^{96} + 680992 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)