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Properties

Label 825.4.cg
Level $825$
Weight $4$
Character orbit 825.cg
Rep. character $\chi_{825}(41,\cdot)$
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.cg (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

\( 1424 q - 7 q^{3} + 5620 q^{4} - 45 q^{6} + 10 q^{7} - 49 q^{9} + O(q^{10}) \) \( 1424 q - 7 q^{3} + 5620 q^{4} - 45 q^{6} + 10 q^{7} - 49 q^{9} - 20 q^{10} - 272 q^{12} + 230 q^{13} - 27 q^{15} + 22124 q^{16} - 10 q^{18} + 135 q^{21} + 478 q^{22} - 370 q^{24} + 156 q^{25} + 443 q^{27} + 190 q^{28} - 45 q^{30} + 208 q^{31} + 219 q^{33} - 28 q^{34} - 841 q^{36} - 254 q^{37} - 5 q^{39} - 1180 q^{40} - 677 q^{42} + 1533 q^{45} + 910 q^{46} - 2396 q^{48} + 15758 q^{49} + 125 q^{51} + 3110 q^{52} - 1460 q^{54} - 36 q^{55} - 570 q^{57} + 876 q^{58} - 1916 q^{60} - 730 q^{61} - 5 q^{63} + 85756 q^{64} - 1930 q^{66} + 720 q^{67} + 1186 q^{69} + 3704 q^{70} - 4370 q^{72} - 10 q^{73} - 1603 q^{75} - 3263 q^{78} - 1480 q^{79} + 31 q^{81} - 5284 q^{82} - 1280 q^{84} - 3370 q^{85} - 270 q^{87} + 7202 q^{88} - 45 q^{90} - 2890 q^{91} - 613 q^{93} + 9570 q^{94} - 3100 q^{96} - 3608 q^{97} + 383 q^{99} + O(q^{100}) \)

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.