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Properties

Label 882.3.i
Level $882$
Weight $3$
Character orbit 882.i
Rep. character $\chi_{882}(569,\cdot)$
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.i (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

\( 160 q + 160 q^{4} - 8 q^{6} + O(q^{10}) \) \( 160 q + 160 q^{4} - 8 q^{6} - 10 q^{13} - 14 q^{15} - 320 q^{16} - 54 q^{17} - 56 q^{18} - 28 q^{19} - 8 q^{24} - 800 q^{25} - 72 q^{26} + 126 q^{27} - 36 q^{29} + 144 q^{30} + 8 q^{31} + 106 q^{33} - 48 q^{36} - 22 q^{37} + 314 q^{39} - 72 q^{41} - 16 q^{43} + 144 q^{44} + 250 q^{45} + 12 q^{46} + 108 q^{47} + 432 q^{50} - 250 q^{51} - 40 q^{52} - 8 q^{54} + 24 q^{55} + 354 q^{57} - 48 q^{58} + 90 q^{59} - 116 q^{60} + 62 q^{61} - 1280 q^{64} - 630 q^{65} - 224 q^{66} - 70 q^{67} - 218 q^{69} - 80 q^{72} - 196 q^{73} - 166 q^{75} + 56 q^{76} - 128 q^{78} + 50 q^{79} - 580 q^{81} - 120 q^{85} + 98 q^{87} - 486 q^{89} - 296 q^{90} - 396 q^{92} + 382 q^{93} - 168 q^{94} - 72 q^{95} + 16 q^{96} + 38 q^{97} - 482 q^{99} + O(q^{100}) \)

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

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