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Properties

Label 882.3.bg
Level $882$
Weight $3$
Character orbit 882.bg
Rep. character $\chi_{882}(103,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1344$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.bg (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(882, [\chi])\).

Total New Old
Modular forms 4080 1344 2736
Cusp forms 3984 1344 2640
Eisenstein series 96 0 96

Trace form

\( 1344 q - 448 q^{4} - 28 q^{6} + 2 q^{7} + 40 q^{9} + O(q^{10}) \) \( 1344 q - 448 q^{4} - 28 q^{6} + 2 q^{7} + 40 q^{9} - 30 q^{13} + 12 q^{14} + 6 q^{15} - 896 q^{16} - 54 q^{17} - 16 q^{18} + 12 q^{21} - 234 q^{23} - 560 q^{25} + 72 q^{26} - 294 q^{27} + 4 q^{28} - 156 q^{29} + 4 q^{30} + 66 q^{35} + 80 q^{36} - 286 q^{37} - 38 q^{39} + 396 q^{41} - 112 q^{42} + 16 q^{43} + 688 q^{45} + 156 q^{46} - 252 q^{47} - 50 q^{49} + 48 q^{50} + 186 q^{51} + 220 q^{52} + 1488 q^{53} + 144 q^{54} - 84 q^{55} + 24 q^{56} - 316 q^{57} - 312 q^{58} + 12 q^{60} - 98 q^{61} - 186 q^{63} - 1792 q^{64} - 84 q^{65} - 96 q^{66} + 140 q^{67} - 108 q^{68} - 154 q^{69} - 72 q^{70} - 546 q^{71} - 32 q^{72} + 72 q^{74} - 498 q^{75} - 570 q^{77} + 64 q^{78} + 188 q^{79} + 260 q^{81} + 2772 q^{83} + 444 q^{84} + 72 q^{86} - 316 q^{87} + 636 q^{89} - 984 q^{90} + 186 q^{91} + 36 q^{92} + 4 q^{93} - 720 q^{95} + 114 q^{97} - 912 q^{98} - 34 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)