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Properties

Label 825.6.cu
Level $825$
Weight $6$
Character orbit 825.cu
Rep. character $\chi_{825}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4768$
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.cu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 4832 4832 0
Cusp forms 4768 4768 0
Eisenstein series 64 64 0

Trace form

\( 4768 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 240 q^{7} + O(q^{10}) \) \( 4768 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 240 q^{7} + 320 q^{10} + 1442 q^{12} + 1036 q^{13} + 1906 q^{15} + 299004 q^{16} - 518 q^{18} + 8760 q^{19} - 12 q^{21} + 10560 q^{22} - 10240 q^{24} + 1032 q^{25} + 2866 q^{27} - 18892 q^{28} - 12506 q^{30} - 4 q^{31} - 13272 q^{33} - 40 q^{34} + 2046 q^{36} - 46264 q^{37} + 19332 q^{40} - 4986 q^{42} + 46680 q^{43} - 22638 q^{45} - 4 q^{46} - 28986 q^{48} + 86020 q^{49} - 12 q^{51} - 153948 q^{52} - 197060 q^{54} + 948 q^{55} - 173730 q^{57} + 30012 q^{58} - 227000 q^{60} - 24 q^{61} + 15656 q^{63} + 417780 q^{64} + 46650 q^{66} + 109828 q^{67} - 593910 q^{69} - 176680 q^{70} - 20898 q^{72} + 179360 q^{73} - 150766 q^{75} + 24512 q^{76} + 166500 q^{78} + 1044240 q^{79} - 58912 q^{81} + 381212 q^{82} - 77770 q^{84} + 35708 q^{85} + 88734 q^{87} + 625384 q^{88} - 3126334 q^{90} - 4 q^{91} - 104288 q^{93} - 20 q^{94} + 54004 q^{96} - 837616 q^{97} - 830570 q^{99} + O(q^{100}) \)

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.