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Properties

Label 825.4.df
Level $825$
Weight $4$
Character orbit 825.df
Rep. character $\chi_{825}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2848$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 825.df (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
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 2912 2912 0
Cusp forms 2848 2848 0
Eisenstein series 64 64 0

Trace form

\( 2848 q - 2 q^{3} - 20 q^{4} - 12 q^{6} - 48 q^{7} + 150 q^{9} + O(q^{10}) \) \( 2848 q - 2 q^{3} - 20 q^{4} - 12 q^{6} - 48 q^{7} + 150 q^{9} - 200 q^{10} - 140 q^{12} - 108 q^{13} - 14 q^{15} + 11004 q^{16} + 26 q^{18} - 20 q^{19} - 12 q^{21} + 480 q^{22} - 640 q^{24} + 132 q^{25} - 302 q^{27} - 1052 q^{28} + 1994 q^{30} - 4 q^{31} + 1344 q^{33} - 40 q^{34} + 756 q^{36} - 1236 q^{37} - 710 q^{39} - 5708 q^{40} - 2902 q^{42} + 64 q^{43} + 1412 q^{45} - 24 q^{46} + 534 q^{48} - 3060 q^{49} - 12 q^{51} + 356 q^{52} - 2780 q^{54} + 1848 q^{55} + 222 q^{57} + 7716 q^{58} - 4010 q^{60} - 4 q^{61} + 3212 q^{63} - 4180 q^{64} + 1290 q^{66} - 632 q^{67} - 10 q^{69} - 5880 q^{70} - 236 q^{72} + 1404 q^{73} + 4994 q^{75} - 1088 q^{76} + 380 q^{78} + 958 q^{81} + 4604 q^{82} - 2172 q^{85} - 1732 q^{87} + 8552 q^{88} - 16634 q^{90} - 4 q^{91} + 10330 q^{93} - 2466 q^{96} + 1740 q^{97} + O(q^{100}) \)

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.