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Properties

Label 882.5.q
Level $882$
Weight $5$
Character orbit 882.q
Rep. character $\chi_{882}(491,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $328$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 1376 328 1048
Cusp forms 1312 328 984
Eisenstein series 64 0 64

Trace form

\( 328 q + 6 q^{3} + 1312 q^{4} + 18 q^{5} - 80 q^{6} + 162 q^{9} + O(q^{10}) \) \( 328 q + 6 q^{3} + 1312 q^{4} + 18 q^{5} - 80 q^{6} + 162 q^{9} + 216 q^{11} - 144 q^{12} - 10 q^{13} + 154 q^{15} - 10496 q^{16} - 512 q^{18} + 716 q^{19} + 144 q^{20} + 336 q^{22} - 1278 q^{23} - 128 q^{24} + 20794 q^{25} + 1224 q^{27} - 3438 q^{29} + 2112 q^{30} - 742 q^{31} - 1700 q^{33} - 96 q^{34} + 1632 q^{36} - 4168 q^{37} + 6768 q^{38} - 1606 q^{39} + 8892 q^{41} - 772 q^{43} - 11966 q^{45} - 2112 q^{46} - 10314 q^{47} - 1536 q^{48} + 15552 q^{50} + 554 q^{51} + 80 q^{52} - 6320 q^{54} + 1092 q^{55} - 14598 q^{57} + 2400 q^{58} - 10512 q^{59} - 4016 q^{60} + 4478 q^{61} - 167936 q^{64} + 28602 q^{65} + 4192 q^{66} - 7756 q^{67} + 10512 q^{68} + 12106 q^{69} - 8960 q^{72} - 17308 q^{73} + 16992 q^{74} + 5858 q^{75} + 2864 q^{76} + 544 q^{78} + 6050 q^{79} + 56402 q^{81} + 1152 q^{82} - 3834 q^{83} + 1308 q^{85} + 26640 q^{86} - 3730 q^{87} - 2688 q^{88} + 22048 q^{90} - 10224 q^{92} + 30610 q^{93} - 672 q^{94} - 51120 q^{95} + 4096 q^{96} + 18644 q^{97} - 66758 q^{99} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)