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Properties

Label 825.6.j
Level $825$
Weight $6$
Character orbit 825.j
Rep. character $\chi_{825}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $360$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1224 360 864
Cusp forms 1176 360 816
Eisenstein series 48 0 48

Trace form

\( 360 q + O(q^{10}) \) \( 360 q + 80 q^{11} + 1584 q^{12} - 89120 q^{16} + 2908 q^{22} - 10208 q^{23} + 16800 q^{26} + 19360 q^{31} + 15624 q^{33} - 466560 q^{36} + 37048 q^{37} + 74536 q^{38} - 34848 q^{42} + 52800 q^{47} + 50688 q^{48} - 63624 q^{53} + 155600 q^{56} - 316736 q^{58} + 182160 q^{66} - 213408 q^{67} - 287680 q^{71} - 412584 q^{77} - 151416 q^{78} - 2361960 q^{81} + 313992 q^{82} - 482000 q^{86} + 456956 q^{88} - 1980640 q^{91} - 186880 q^{92} - 4752 q^{93} - 77528 q^{97} + O(q^{100}) \)

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

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