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Properties

Label 882.4.ba
Level $882$
Weight $4$
Character orbit 882.ba
Rep. character $\chi_{882}(43,\cdot)$
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.ba (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

\( 2016 q + 672 q^{4} - 20 q^{5} - 40 q^{6} - 12 q^{7} - 70 q^{9} + O(q^{10}) \) \( 2016 q + 672 q^{4} - 20 q^{5} - 40 q^{6} - 12 q^{7} - 70 q^{9} + 48 q^{13} - 44 q^{14} - 168 q^{15} + 2688 q^{16} + 80 q^{17} - 112 q^{18} - 240 q^{19} - 80 q^{20} - 76 q^{21} - 420 q^{23} - 32 q^{24} + 4200 q^{25} + 784 q^{26} + 48 q^{27} + 96 q^{28} + 70 q^{29} + 616 q^{30} - 60 q^{31} - 776 q^{33} - 1612 q^{35} + 560 q^{36} + 1680 q^{37} - 456 q^{38} + 140 q^{39} - 108 q^{41} - 2348 q^{42} + 84 q^{43} + 1432 q^{45} + 2520 q^{46} - 330 q^{47} + 438 q^{49} + 224 q^{50} - 1092 q^{51} - 480 q^{52} + 7056 q^{53} + 328 q^{54} - 3060 q^{55} - 176 q^{56} + 5712 q^{57} + 1260 q^{58} + 292 q^{59} + 1344 q^{60} + 4164 q^{61} + 3952 q^{62} + 1374 q^{63} - 21504 q^{64} + 1568 q^{65} + 64 q^{66} - 1176 q^{67} + 3648 q^{68} - 4020 q^{69} - 216 q^{70} - 10360 q^{71} - 448 q^{72} + 1344 q^{73} - 840 q^{74} + 734 q^{75} + 480 q^{76} - 92 q^{77} - 224 q^{78} + 1092 q^{79} - 3840 q^{80} - 4522 q^{81} - 716 q^{83} - 520 q^{84} + 1904 q^{86} + 3432 q^{87} - 9752 q^{89} - 5348 q^{90} - 1500 q^{91} + 672 q^{92} - 8792 q^{93} - 1224 q^{94} - 1484 q^{95} - 128 q^{96} + 1056 q^{97} + 20944 q^{98} - 35392 q^{99} + O(q^{100}) \)

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

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