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Properties

Label 882.3.j
Level $882$
Weight $3$
Character orbit 882.j
Rep. character $\chi_{882}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 704 160 544
Cusp forms 640 160 480
Eisenstein series 64 0 64

Trace form

\( 160 q - 160 q^{4} + 16 q^{9} + O(q^{10}) \) \( 160 q - 160 q^{4} + 16 q^{9} - 48 q^{11} + 30 q^{13} - 66 q^{15} - 320 q^{16} - 54 q^{17} - 56 q^{18} - 132 q^{23} + 24 q^{24} - 800 q^{25} + 72 q^{26} - 126 q^{27} + 156 q^{29} - 64 q^{30} + 24 q^{31} - 126 q^{33} - 16 q^{36} + 22 q^{37} - 298 q^{39} - 396 q^{41} + 16 q^{43} + 48 q^{44} + 258 q^{45} - 12 q^{46} - 108 q^{47} + 144 q^{50} + 294 q^{51} + 276 q^{53} + 144 q^{54} + 406 q^{57} - 48 q^{58} + 90 q^{59} + 204 q^{60} + 102 q^{61} + 1280 q^{64} - 30 q^{65} - 336 q^{66} - 70 q^{67} + 210 q^{69} - 684 q^{71} + 80 q^{72} - 144 q^{74} - 390 q^{75} - 256 q^{78} - 118 q^{79} + 60 q^{81} + 756 q^{83} + 120 q^{85} - 336 q^{86} - 258 q^{87} - 414 q^{89} - 360 q^{90} + 132 q^{92} - 42 q^{93} + 744 q^{95} - 48 q^{96} - 114 q^{97} - 34 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)