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Properties

Label 882.5.s
Level $882$
Weight $5$
Character orbit 882.s
Rep. character $\chi_{882}(557,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(882, [\chi])\).

Total New Old
Modular forms 1408 104 1304
Cusp forms 1280 104 1176
Eisenstein series 128 0 128

Trace form

\( 104 q + 416 q^{4} + O(q^{10}) \) \( 104 q + 416 q^{4} + 64 q^{10} - 728 q^{13} - 3328 q^{16} + 828 q^{19} - 3840 q^{22} + 2956 q^{25} - 2108 q^{31} + 2048 q^{34} + 6204 q^{37} - 512 q^{40} + 19512 q^{43} - 3584 q^{46} - 2912 q^{52} + 48224 q^{55} + 9536 q^{58} - 24656 q^{61} - 53248 q^{64} - 18268 q^{67} + 2564 q^{73} + 13248 q^{76} - 1260 q^{79} - 19968 q^{82} - 35840 q^{85} - 15360 q^{88} + 19584 q^{94} + 154256 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{5}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)