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Properties

Label 825.6.c
Level $825$
Weight $6$
Character orbit 825.c
Rep. character $\chi_{825}(199,\cdot)$
Character field $\Q$
Dimension $148$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 612 148 464
Cusp forms 588 148 440
Eisenstein series 24 0 24

Trace form

\( 148 q - 2344 q^{4} - 360 q^{6} - 11988 q^{9} + O(q^{10}) \) \( 148 q - 2344 q^{4} - 360 q^{6} - 11988 q^{9} - 7976 q^{14} + 37016 q^{16} + 5940 q^{19} + 180 q^{21} + 1080 q^{24} - 31024 q^{26} - 3632 q^{29} - 29324 q^{31} - 54048 q^{34} + 189864 q^{36} - 5580 q^{39} + 28112 q^{41} - 9680 q^{44} + 69240 q^{46} - 272792 q^{49} + 20880 q^{51} + 29160 q^{54} + 339720 q^{56} - 164128 q^{59} + 218068 q^{61} - 251352 q^{64} - 34848 q^{66} + 120816 q^{69} - 95520 q^{71} - 640544 q^{74} + 151256 q^{76} + 71472 q^{79} + 971028 q^{81} + 19872 q^{84} - 143880 q^{86} - 468776 q^{89} - 281212 q^{91} + 151752 q^{94} - 50760 q^{96} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)