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Properties

Label 882.4.bb
Level $882$
Weight $4$
Character orbit 882.bb
Rep. character $\chi_{882}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $2016$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.bb (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(882, [\chi])\).

Total New Old
Modular forms 6096 2016 4080
Cusp forms 6000 2016 3984
Eisenstein series 96 0 96

Trace form

\( 2016 q - 1344 q^{4} - 20 q^{5} + 20 q^{6} - 12 q^{7} - 70 q^{9} + O(q^{10}) \) \( 2016 q - 1344 q^{4} - 20 q^{5} + 20 q^{6} - 12 q^{7} - 70 q^{9} - 24 q^{13} - 44 q^{14} + 84 q^{15} - 5376 q^{16} - 184 q^{17} - 112 q^{18} + 120 q^{19} - 80 q^{20} - 64 q^{21} + 1092 q^{23} - 32 q^{24} + 4200 q^{25} - 272 q^{26} + 246 q^{27} - 48 q^{28} - 182 q^{29} - 56 q^{30} - 60 q^{31} - 200 q^{33} + 824 q^{35} - 280 q^{36} + 2184 q^{37} - 456 q^{38} + 350 q^{39} - 930 q^{41} + 2428 q^{42} - 42 q^{43} - 1814 q^{45} + 3276 q^{46} - 330 q^{47} + 438 q^{49} - 112 q^{50} + 168 q^{51} + 1248 q^{52} - 4116 q^{53} - 1196 q^{54} + 1530 q^{55} - 176 q^{56} - 2856 q^{57} - 3276 q^{58} + 2416 q^{59} + 336 q^{60} + 4164 q^{61} + 1000 q^{62} + 4302 q^{63} - 21504 q^{64} + 1568 q^{65} + 1984 q^{66} - 1176 q^{67} + 3072 q^{68} + 3972 q^{69} + 324 q^{70} + 5180 q^{71} - 448 q^{72} - 672 q^{73} + 420 q^{74} - 2788 q^{75} + 480 q^{76} + 1276 q^{77} + 112 q^{78} + 1092 q^{79} + 1920 q^{80} - 1834 q^{81} - 1724 q^{83} - 928 q^{84} - 952 q^{86} - 7068 q^{87} + 8638 q^{89} + 15676 q^{90} + 750 q^{91} - 336 q^{92} - 15176 q^{93} + 2448 q^{94} - 1484 q^{95} - 128 q^{96} - 528 q^{97} - 12704 q^{98} + 17696 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

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