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Properties

Label 825.4.s
Level $825$
Weight $4$
Character orbit 825.s
Rep. character $\chi_{825}(479,\cdot)$
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.s (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

\( 1424 q - 15 q^{3} - 5644 q^{4} + 35 q^{6} - 30 q^{7} - 49 q^{9} + O(q^{10}) \) \( 1424 q - 15 q^{3} - 5644 q^{4} + 35 q^{6} - 30 q^{7} - 49 q^{9} + 140 q^{10} + 190 q^{12} - 10 q^{13} + 13 q^{15} + 21884 q^{16} - 135 q^{21} - 430 q^{22} - 290 q^{24} - 312 q^{25} + 735 q^{27} + 350 q^{28} + 35 q^{30} - 212 q^{31} - 805 q^{33} + 4 q^{34} + 711 q^{36} - 550 q^{37} - 5 q^{39} - 120 q^{40} + 1555 q^{42} + 129 q^{45} - 930 q^{46} - 1980 q^{48} - 16778 q^{49} - 145 q^{51} - 570 q^{52} - 1300 q^{54} - 1680 q^{55} - 2430 q^{60} + 710 q^{61} - 5 q^{63} - 81988 q^{64} + 2788 q^{66} - 2840 q^{67} + 42 q^{69} - 324 q^{70} + 4280 q^{72} - 10 q^{73} - 3403 q^{75} + 1875 q^{78} - 1480 q^{79} + 927 q^{81} + 80 q^{82} + 2150 q^{84} + 3350 q^{85} + 10230 q^{88} + 35 q^{90} + 2886 q^{91} + 3545 q^{93} + 9730 q^{94} + 2450 q^{96} + 12260 q^{97} + 383 q^{99} + O(q^{100}) \)

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.