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Properties

Label 825.4.bo
Level $825$
Weight $4$
Character orbit 825.bo
Rep. character $\chi_{825}(134,\cdot)$
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.bo (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

\( 1424 q + 5 q^{3} + 1406 q^{4} - 30 q^{7} - 49 q^{9} + O(q^{10}) \) \( 1424 q + 5 q^{3} + 1406 q^{4} - 30 q^{7} - 49 q^{9} - 180 q^{10} + 110 q^{12} - 10 q^{13} + 13 q^{15} - 5526 q^{16} - 10 q^{19} + 890 q^{22} + 310 q^{24} + 318 q^{25} - 745 q^{27} + 350 q^{28} - 5 q^{30} - 32 q^{31} - 670 q^{33} + 4 q^{34} - 934 q^{36} + 210 q^{39} - 1260 q^{40} + 1305 q^{42} + 1200 q^{43} - 596 q^{45} + 315 q^{48} - 15818 q^{49} + 125 q^{51} + 1260 q^{52} + 1380 q^{54} - 1050 q^{55} + 3330 q^{58} - 420 q^{60} - 730 q^{61} + 1710 q^{63} + 22102 q^{64} - 1407 q^{66} - 2960 q^{67} + 1612 q^{69} - 2354 q^{70} - 1730 q^{72} - 10 q^{73} - 2333 q^{75} + 4610 q^{78} - 1313 q^{81} + 80 q^{82} + 5390 q^{85} - 5130 q^{88} - 2945 q^{90} - 904 q^{91} + 3555 q^{93} - 6295 q^{96} - 302 q^{99} + O(q^{100}) \)

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.