Properties

Label 800.6.o
Level $800$
Weight $6$
Character orbit 800.o
Rep. character $\chi_{800}(143,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
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.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1248 184 1064
Cusp forms 1152 176 976
Eisenstein series 96 8 88

Trace form

\( 176 q - 4 q^{3} + O(q^{10}) \) \( 176 q - 4 q^{3} + 8 q^{11} + 408 q^{17} + 968 q^{27} + 976 q^{33} - 8 q^{41} + 1308 q^{43} + 41768 q^{51} - 968 q^{57} + 89252 q^{67} + 25184 q^{73} - 1124152 q^{81} - 126444 q^{83} + 658888 q^{91} - 212576 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)