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Properties

Label 882.5.i
Level $882$
Weight $5$
Character orbit 882.i
Rep. character $\chi_{882}(569,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 320 1056
Cusp forms 1312 320 992
Eisenstein series 64 0 64

Trace form

\( 320 q + 1280 q^{4} + 64 q^{6} - 120 q^{9} + O(q^{10}) \) \( 320 q + 1280 q^{4} + 64 q^{6} - 120 q^{9} + 10 q^{13} - 458 q^{15} - 10240 q^{16} + 1350 q^{17} + 1024 q^{18} - 308 q^{19} + 256 q^{24} - 40000 q^{25} + 1152 q^{26} - 1890 q^{27} + 792 q^{29} + 3168 q^{30} - 368 q^{31} - 842 q^{33} + 1344 q^{36} - 1034 q^{37} + 6470 q^{39} - 4464 q^{41} + 352 q^{43} - 7488 q^{44} - 8630 q^{45} - 1056 q^{46} - 6264 q^{47} + 3456 q^{50} - 11746 q^{51} + 160 q^{52} - 19440 q^{53} - 7040 q^{54} - 2544 q^{55} - 5970 q^{57} + 4800 q^{58} - 9810 q^{59} - 1520 q^{60} - 4478 q^{61} - 163840 q^{64} - 5418 q^{65} - 896 q^{66} + 7630 q^{67} + 23458 q^{69} + 7168 q^{72} + 19012 q^{73} - 26506 q^{75} + 2464 q^{76} - 41216 q^{78} - 11702 q^{79} + 18944 q^{81} + 17400 q^{85} - 69034 q^{87} - 16038 q^{89} - 15104 q^{90} + 27504 q^{92} - 52670 q^{93} - 1344 q^{94} + 42192 q^{95} - 2048 q^{96} + 6346 q^{97} - 13430 q^{99} + O(q^{100}) \)

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

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