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Properties

Label 825.6.bu
Level $825$
Weight $6$
Character orbit 825.bu
Rep. character $\chi_{825}(239,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2384$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 825.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(825, [\chi])\).

Total New Old
Modular forms 2416 2416 0
Cusp forms 2384 2384 0
Eisenstein series 32 32 0

Trace form

\( 2384 q + 9470 q^{4} - 165 q^{6} + 190 q^{7} + 56 q^{9} + O(q^{10}) \) \( 2384 q + 9470 q^{4} - 165 q^{6} + 190 q^{7} + 56 q^{9} + 920 q^{10} - 170 q^{12} - 20 q^{13} + 1908 q^{15} - 148486 q^{16} - 4400 q^{19} + 1215 q^{21} + 6970 q^{22} - 4970 q^{24} - 8514 q^{25} + 9110 q^{28} + 1210 q^{30} + 9978 q^{31} + 23555 q^{33} + 52 q^{34} - 5121 q^{36} - 32790 q^{37} - 10 q^{40} + 87485 q^{42} + 12063 q^{45} - 10 q^{46} + 1210 q^{48} - 1364782 q^{49} - 1225 q^{51} - 108270 q^{52} - 98840 q^{54} - 226716 q^{55} - 10 q^{58} - 173291 q^{60} - 84040 q^{63} + 2291106 q^{64} - 107625 q^{66} - 84430 q^{67} + 223476 q^{69} - 63246 q^{70} + 163835 q^{72} - 10 q^{73} + 205282 q^{75} - 169905 q^{78} - 522140 q^{79} + 6096 q^{81} - 320 q^{82} + 47580 q^{84} - 239240 q^{85} + 226550 q^{88} - 1039195 q^{90} + 182840 q^{91} + 336055 q^{93} - 330 q^{94} - 10 q^{97} + 447143 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.