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Properties

Label 825.6.cs
Level $825$
Weight $6$
Character orbit 825.cs
Rep. character $\chi_{825}(23,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4000$
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.cs (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
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 4000 832
Cusp forms 4768 4000 768
Eisenstein series 64 0 64

Trace form

\( 4000 q + 2 q^{3} + O(q^{10}) \) \( 4000 q + 2 q^{3} - 128 q^{12} - 3184 q^{13} - 4084 q^{15} + 256000 q^{16} + 12132 q^{18} - 26448 q^{25} - 23044 q^{27} - 22432 q^{28} - 39256 q^{30} - 7502 q^{33} - 76480 q^{34} + 65196 q^{37} + 14320 q^{39} + 62312 q^{40} + 268544 q^{42} - 33848 q^{45} - 441196 q^{48} + 254392 q^{52} + 132340 q^{54} + 27588 q^{55} - 213400 q^{57} - 296968 q^{58} + 828640 q^{60} - 293604 q^{63} + 48188 q^{67} + 29540 q^{69} + 800040 q^{70} + 863512 q^{72} + 156880 q^{73} - 118516 q^{75} + 1026760 q^{78} + 75280 q^{79} + 58900 q^{81} + 82872 q^{82} - 1954560 q^{84} + 782728 q^{85} - 1370076 q^{87} + 917664 q^{88} + 594976 q^{90} + 233592 q^{93} + 492364 q^{97} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)