↑

Properties

Label 825.6.ct
Level $825$
Weight $6$
Character orbit 825.ct
Rep. character $\chi_{825}(218,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2848$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 825.ct (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(825, [\chi])\).

Total New Old
Modular forms 4896 2912 1984
Cusp forms 4704 2848 1856
Eisenstein series 192 64 128

Trace form

\( 2848 q + 8 q^{3} - 12 q^{6} - 140 q^{7} + O(q^{10}) \) \( 2848 q + 8 q^{3} - 12 q^{6} - 140 q^{7} + 1628 q^{12} - 1036 q^{13} + 176104 q^{16} - 122 q^{18} + 3888 q^{21} + 3400 q^{22} - 2866 q^{27} + 18892 q^{28} - 19384 q^{31} - 36278 q^{33} - 105004 q^{36} + 46264 q^{37} - 73094 q^{42} - 81920 q^{43} + 125736 q^{46} + 18746 q^{48} - 260372 q^{51} - 209772 q^{52} + 173730 q^{57} - 147052 q^{58} + 136536 q^{61} + 152414 q^{63} + 180280 q^{66} - 8448 q^{67} + 143068 q^{72} - 179360 q^{73} - 303968 q^{76} - 166820 q^{78} - 222152 q^{81} - 380572 q^{82} - 91164 q^{87} + 1922416 q^{88} - 236744 q^{91} - 61372 q^{93} + 941324 q^{96} + 389256 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)