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Properties

Label 882.5.bm
Level $882$
Weight $5$
Character orbit 882.bm
Rep. character $\chi_{882}(61,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2688$
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.bm (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 8112 2688 5424
Cusp forms 8016 2688 5328
Eisenstein series 96 0 96

Trace form

\( 2688 q + 1792 q^{4} + 224 q^{6} - 26 q^{7} + 208 q^{9} + O(q^{10}) \) \( 2688 q + 1792 q^{4} + 224 q^{6} - 26 q^{7} + 208 q^{9} - 30 q^{13} + 96 q^{14} - 174 q^{15} + 14336 q^{16} + 1350 q^{17} - 256 q^{18} + 504 q^{21} - 3330 q^{23} - 768 q^{24} + 56000 q^{25} - 1152 q^{26} - 1680 q^{27} - 208 q^{28} - 2112 q^{29} + 544 q^{30} - 1104 q^{31} + 2142 q^{33} + 1806 q^{35} - 640 q^{36} - 13442 q^{37} + 4426 q^{39} - 4140 q^{41} - 13504 q^{42} - 352 q^{43} + 10252 q^{45} - 13728 q^{46} - 22968 q^{47} - 5782 q^{49} - 3072 q^{50} + 1374 q^{51} + 560 q^{52} - 34176 q^{53} - 6336 q^{54} + 8904 q^{55} - 1536 q^{56} - 25780 q^{57} - 12000 q^{58} - 9810 q^{59} - 1392 q^{60} - 26986 q^{61} - 11886 q^{63} - 229376 q^{64} - 5082 q^{65} + 18816 q^{66} + 7630 q^{67} - 31234 q^{69} - 6048 q^{70} - 27174 q^{71} - 2048 q^{72} + 576 q^{74} - 5562 q^{75} - 9402 q^{77} - 5888 q^{78} - 974 q^{79} + 34424 q^{81} + 85680 q^{83} + 42720 q^{84} - 21888 q^{86} - 35326 q^{87} + 23088 q^{89} + 41856 q^{90} - 7026 q^{91} - 5328 q^{92} + 250342 q^{93} - 34704 q^{95} + 6144 q^{96} - 19038 q^{97} - 92544 q^{98} - 21190 q^{99} + O(q^{100}) \)

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

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