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Properties

Label 825.6.cv
Level $825$
Weight $6$
Character orbit 825.cv
Rep. character $\chi_{825}(38,\cdot)$
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.cv (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

\( 4768 q - 8 q^{3} - 20 q^{4} - 2 q^{6} + 140 q^{7} - 10 q^{9} + O(q^{10}) \) \( 4768 q - 8 q^{3} - 20 q^{4} - 2 q^{6} + 140 q^{7} - 10 q^{9} + 680 q^{10} - 668 q^{12} - 1584 q^{13} - 7654 q^{15} + 299004 q^{16} + 122 q^{18} + 8760 q^{19} - 12 q^{21} - 10520 q^{22} + 10240 q^{24} - 11728 q^{25} + 2866 q^{27} - 18892 q^{28} - 12506 q^{30} - 24 q^{31} - 13272 q^{33} - 40 q^{34} - 8194 q^{36} - 46264 q^{37} + 38940 q^{39} + 19332 q^{40} - 29306 q^{42} - 87720 q^{43} + 8612 q^{45} - 4 q^{46} - 31416 q^{48} - 137940 q^{49} - 12 q^{51} + 42092 q^{52} + 197020 q^{54} - 61552 q^{55} - 173730 q^{57} + 147052 q^{58} - 227000 q^{60} - 4 q^{61} - 152414 q^{63} + 419300 q^{64} - 31110 q^{66} - 232492 q^{67} + 593890 q^{69} - 27940 q^{70} - 20898 q^{72} - 816020 q^{73} - 693206 q^{75} - 16448 q^{76} + 7220 q^{78} - 20 q^{79} - 58902 q^{81} + 381212 q^{82} - 10 q^{84} + 35708 q^{85} - 134356 q^{87} + 171624 q^{88} - 738124 q^{90} - 24 q^{91} - 106718 q^{93} - 675100 q^{94} + 54014 q^{96} - 307756 q^{97} + O(q^{100}) \)

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.