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Properties

Label 825.4.br
Level $825$
Weight $4$
Character orbit 825.br
Rep. character $\chi_{825}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1424$
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.br (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1456 1456 0
Cusp forms 1424 1424 0
Eisenstein series 32 32 0

Trace form

\( 1424 q - 5 q^{3} + 1406 q^{4} - 5 q^{6} + 30 q^{7} + 31 q^{9} + O(q^{10}) \) \( 1424 q - 5 q^{3} + 1406 q^{4} - 5 q^{6} + 30 q^{7} + 31 q^{9} + 180 q^{10} + 110 q^{12} - 10 q^{13} - 102 q^{15} - 5526 q^{16} - 70 q^{19} + 410 q^{22} + 310 q^{24} - 312 q^{25} - 5 q^{27} + 700 q^{28} + 735 q^{30} - 912 q^{31} - 805 q^{33} + 4 q^{34} + 1031 q^{36} - 10 q^{37} - 220 q^{39} - 10 q^{40} - 1200 q^{43} - 596 q^{45} + 1070 q^{46} - 15818 q^{49} + 125 q^{51} + 2250 q^{52} - 1380 q^{54} - 270 q^{55} + 70 q^{58} + 3220 q^{60} - 10 q^{61} - 10 q^{63} + 19762 q^{64} - 287 q^{66} - 2960 q^{67} - 1503 q^{69} - 2344 q^{70} - 5130 q^{72} - 20 q^{73} + 87 q^{75} + 4610 q^{78} - 10 q^{79} + 127 q^{81} - 80 q^{82} + 1440 q^{84} + 6770 q^{85} + 8550 q^{88} - 8460 q^{90} + 2876 q^{91} - 3555 q^{93} - 9670 q^{94} + 9355 q^{96} + 740 q^{97} - 302 q^{99} + O(q^{100}) \)

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.