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Properties

Label 882.5.x
Level $882$
Weight $5$
Character orbit 882.x
Rep. character $\chi_{882}(71,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $432$
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.x (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 4080 432 3648
Cusp forms 3984 432 3552
Eisenstein series 96 0 96

Trace form

\( 432 q + 576 q^{4} + O(q^{10}) \) \( 432 q + 576 q^{4} + 128 q^{10} - 560 q^{13} - 4608 q^{16} + 1040 q^{19} - 3200 q^{22} + 6264 q^{25} + 880 q^{31} - 2048 q^{34} - 1408 q^{37} + 2560 q^{40} - 7680 q^{43} - 13608 q^{49} - 11200 q^{52} - 16808 q^{55} - 14400 q^{58} + 37152 q^{61} + 36864 q^{64} - 17648 q^{67} + 45696 q^{70} + 27360 q^{73} - 8320 q^{76} + 5488 q^{79} - 18432 q^{82} + 76160 q^{85} - 10240 q^{88} + 18368 q^{91} + 640 q^{94} - 7872 q^{97} + O(q^{100}) \)

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

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