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Properties

Label 882.3.o
Level $882$
Weight $3$
Character orbit 882.o
Rep. character $\chi_{882}(97,\cdot)$
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.o (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

\( 160 q - 160 q^{4} - 32 q^{9} + O(q^{10}) \) \( 160 q - 160 q^{4} - 32 q^{9} + 24 q^{11} - 84 q^{15} - 320 q^{16} + 16 q^{18} + 12 q^{23} + 400 q^{25} + 120 q^{29} + 200 q^{30} + 80 q^{36} + 88 q^{37} - 280 q^{39} - 32 q^{43} - 96 q^{44} - 48 q^{46} + 360 q^{51} + 816 q^{53} - 284 q^{57} - 48 q^{58} + 1280 q^{64} - 156 q^{65} + 140 q^{67} - 936 q^{71} - 160 q^{72} - 144 q^{74} - 448 q^{78} + 164 q^{79} + 696 q^{81} + 120 q^{85} - 48 q^{86} + 24 q^{92} + 744 q^{93} - 336 q^{95} + 740 q^{99} + O(q^{100}) \)

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

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