↑

Properties

Label 825.4.ct
Level $825$
Weight $4$
Character orbit 825.ct
Rep. character $\chi_{825}(218,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1696$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 825.ct (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(825, [\chi])\).

Total New Old
Modular forms 2976 1760 1216
Cusp forms 2784 1696 1088
Eisenstein series 192 64 128

Trace form

\( 1696 q + 2 q^{3} - 12 q^{6} - 12 q^{7} + O(q^{10}) \) \( 1696 q + 2 q^{3} - 12 q^{6} - 12 q^{7} - 100 q^{12} + 108 q^{13} + 6376 q^{16} - 26 q^{18} - 480 q^{21} - 480 q^{22} + 302 q^{27} + 892 q^{28} + 840 q^{31} + 1546 q^{33} - 1324 q^{36} - 564 q^{37} + 202 q^{42} - 1984 q^{43} - 888 q^{46} + 986 q^{48} + 4252 q^{51} + 84 q^{52} - 222 q^{57} + 4844 q^{58} + 552 q^{61} + 218 q^{63} + 1360 q^{66} - 448 q^{67} + 316 q^{72} + 5976 q^{73} - 3680 q^{76} + 4540 q^{78} - 4556 q^{81} - 4604 q^{82} - 1308 q^{87} - 22672 q^{88} + 14664 q^{91} - 7390 q^{93} + 18956 q^{96} - 1740 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)