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Properties

Label 825.6.cw
Level $825$
Weight $6$
Character orbit 825.cw
Rep. character $\chi_{825}(7,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1440$
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.cw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 4896 1440 3456
Cusp forms 4704 1440 3264
Eisenstein series 192 0 192

Trace form

\( 1440 q - 1180 q^{7} + O(q^{10}) \) \( 1440 q - 1180 q^{7} - 80 q^{11} - 1584 q^{12} + 89120 q^{16} + 3820 q^{17} - 2908 q^{22} + 10208 q^{23} - 16800 q^{26} - 18240 q^{28} - 19360 q^{31} - 15624 q^{33} + 466560 q^{36} - 37048 q^{37} - 74536 q^{38} + 289200 q^{41} - 52272 q^{42} + 95000 q^{46} + 85140 q^{47} + 76032 q^{48} - 104400 q^{51} + 28360 q^{52} - 95436 q^{53} - 420400 q^{56} - 71640 q^{57} + 300016 q^{58} + 227600 q^{61} + 317120 q^{62} + 95580 q^{63} + 91440 q^{66} + 509488 q^{67} - 244480 q^{68} + 287680 q^{71} + 49260 q^{73} + 412584 q^{77} - 605664 q^{78} + 2361960 q^{81} + 452048 q^{82} + 632200 q^{83} + 482000 q^{86} - 157716 q^{88} - 3760 q^{91} - 1035220 q^{92} - 7128 q^{93} + 1488608 q^{97} + O(q^{100}) \)

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

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