Properties

Label 882.5.bn
Level $882$
Weight $5$
Character orbit 882.bn
Rep. character $\chi_{882}(65,\cdot)$
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.bn (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

\( 2688 q - 1792 q^{4} - 160 q^{6} + 26 q^{7} - 208 q^{9} + O(q^{10}) \) \( 2688 q - 1792 q^{4} - 160 q^{6} + 26 q^{7} - 208 q^{9} + 10 q^{13} - 288 q^{14} + 174 q^{15} + 14336 q^{16} + 1350 q^{17} - 256 q^{18} - 308 q^{19} - 808 q^{21} - 13986 q^{23} + 256 q^{24} + 56000 q^{25} + 1152 q^{26} - 7980 q^{27} - 208 q^{28} - 4752 q^{29} + 2656 q^{30} - 368 q^{31} - 842 q^{33} + 5490 q^{35} - 640 q^{36} + 13442 q^{37} - 874 q^{39} - 4464 q^{41} - 25664 q^{42} + 352 q^{43} + 28036 q^{45} + 13728 q^{46} - 6264 q^{47} + 2090 q^{49} - 9216 q^{50} + 1374 q^{51} - 400 q^{52} - 5472 q^{53} - 7040 q^{54} + 6360 q^{55} - 23520 q^{57} - 12000 q^{58} - 9810 q^{59} - 1392 q^{60} + 19238 q^{61} - 6594 q^{63} + 229376 q^{64} + 15246 q^{65} - 896 q^{66} + 7630 q^{67} + 15954 q^{69} - 6048 q^{70} + 156870 q^{71} + 2048 q^{72} + 19012 q^{73} - 28354 q^{75} + 2464 q^{76} - 7794 q^{77} - 5888 q^{78} - 7934 q^{79} - 17992 q^{81} - 56416 q^{84} - 27594 q^{87} + 132012 q^{89} - 66176 q^{90} - 11762 q^{91} + 15984 q^{92} - 3842 q^{93} - 1344 q^{94} - 9936 q^{95} - 2048 q^{96} + 6346 q^{97} - 14976 q^{98} + 54458 q^{99} + O(q^{100}) \)

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

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