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Properties

Label 882.3.p
Level $882$
Weight $3$
Character orbit 882.p
Rep. character $\chi_{882}(607,\cdot)$
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.p (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

\( 160 q + 320 q^{4} - 8 q^{9} + O(q^{10}) \) \( 160 q + 320 q^{4} - 8 q^{9} + 24 q^{11} - 30 q^{13} - 66 q^{15} + 640 q^{16} - 54 q^{17} + 16 q^{18} + 66 q^{23} + 400 q^{25} + 72 q^{26} + 126 q^{27} + 156 q^{29} + 68 q^{30} - 16 q^{36} + 22 q^{37} + 242 q^{39} + 396 q^{41} + 16 q^{43} + 48 q^{44} + 156 q^{45} - 12 q^{46} + 144 q^{50} - 78 q^{51} - 60 q^{52} + 276 q^{53} + 144 q^{54} + 406 q^{57} + 24 q^{58} - 132 q^{60} + 1280 q^{64} + 60 q^{65} - 96 q^{66} + 140 q^{67} - 108 q^{68} - 210 q^{69} - 684 q^{71} + 32 q^{72} + 72 q^{74} - 582 q^{75} - 256 q^{78} + 236 q^{79} - 720 q^{81} - 756 q^{83} + 120 q^{85} + 168 q^{86} - 876 q^{87} - 414 q^{89} + 360 q^{90} + 132 q^{92} - 450 q^{93} - 1488 q^{95} + 114 q^{97} - 34 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)