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Properties

Label 825.6.f
Level $825$
Weight $6$
Character orbit 825.f
Rep. character $\chi_{825}(626,\cdot)$
Character field $\Q$
Dimension $374$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 612 386 226
Cusp forms 588 374 214
Eisenstein series 24 12 12

Trace form

\( 374 q - 21 q^{3} + 5892 q^{4} - 121 q^{9} + O(q^{10}) \) \( 374 q - 21 q^{3} + 5892 q^{4} - 121 q^{9} - 568 q^{12} + 97148 q^{16} + 1960 q^{22} + 6828 q^{27} - 10538 q^{31} + 121 q^{33} - 37800 q^{34} + 21692 q^{36} + 634 q^{37} + 54800 q^{42} - 15084 q^{48} - 835134 q^{49} + 61880 q^{58} + 1644420 q^{64} + 80154 q^{66} + 36226 q^{67} + 112607 q^{69} + 193040 q^{78} + 165567 q^{81} + 232720 q^{82} + 54880 q^{88} + 281136 q^{91} - 153315 q^{93} - 742494 q^{97} - 134157 q^{99} + O(q^{100}) \)

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

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