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Properties

Label 825.6.bx
Level $825$
Weight $6$
Character orbit 825.bx
Rep. character $\chi_{825}(49,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $720$
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.bx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 720 1728
Cusp forms 2352 720 1632
Eisenstein series 96 0 96

Trace form

\( 720 q + 2880 q^{4} - 144 q^{6} + 14580 q^{9} + O(q^{10}) \) \( 720 q + 2880 q^{4} - 144 q^{6} + 14580 q^{9} + 356 q^{11} - 7760 q^{14} - 55256 q^{16} + 8584 q^{19} + 14112 q^{21} + 6912 q^{24} - 54380 q^{26} + 29612 q^{31} - 31360 q^{34} - 233280 q^{36} + 46656 q^{39} - 68304 q^{41} - 28356 q^{44} + 138028 q^{46} + 233872 q^{49} - 72936 q^{51} - 46656 q^{54} - 633240 q^{56} - 132756 q^{59} + 140692 q^{61} + 1192696 q^{64} + 89712 q^{66} - 18612 q^{69} + 72816 q^{71} - 340272 q^{74} + 497768 q^{76} + 271608 q^{79} - 1180980 q^{81} + 495504 q^{84} - 18608 q^{86} + 162800 q^{89} - 904580 q^{91} + 1243044 q^{94} - 258048 q^{96} - 28836 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)