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Properties

Label 825.6.bi
Level $825$
Weight $6$
Character orbit 825.bi
Rep. character $\chi_{825}(101,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1496$
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.bi (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 2448 1544 904
Cusp forms 2352 1496 856
Eisenstein series 96 48 48

Trace form

\( 1496 q + 26 q^{3} - 5882 q^{4} + 5 q^{6} + 10 q^{7} - 424 q^{9} + O(q^{10}) \) \( 1496 q + 26 q^{3} - 5882 q^{4} + 5 q^{6} + 10 q^{7} - 424 q^{9} + 258 q^{12} + 10 q^{13} - 90798 q^{16} + 4825 q^{18} + 4480 q^{19} + 10620 q^{22} - 475 q^{24} + 3242 q^{27} - 46350 q^{28} - 14792 q^{31} + 42494 q^{33} + 22540 q^{34} + 48253 q^{36} + 7186 q^{37} + 30970 q^{39} + 52230 q^{42} + 52050 q^{46} - 16696 q^{48} + 861104 q^{49} + 68640 q^{51} + 14190 q^{52} - 21720 q^{57} - 9950 q^{58} + 35890 q^{61} - 120320 q^{63} - 1206910 q^{64} - 132744 q^{66} + 139404 q^{67} - 115282 q^{69} - 105880 q^{72} + 67200 q^{73} + 258580 q^{78} - 422370 q^{79} - 209252 q^{81} - 68260 q^{82} - 712580 q^{84} - 409730 q^{88} - 192726 q^{91} + 186100 q^{93} + 211550 q^{94} + 1246410 q^{96} - 494446 q^{97} + 1009312 q^{99} + O(q^{100}) \)

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.

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

\( S_{6}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)