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Properties

Label 882.4.bj
Level $882$
Weight $4$
Character orbit 882.bj
Rep. character $\chi_{882}(41,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2016$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.bj (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(882, [\chi])\).

Total New Old
Modular forms 6096 2016 4080
Cusp forms 6000 2016 3984
Eisenstein series 96 0 96

Trace form

\( 2016 q - 672 q^{4} + 56 q^{6} + 12 q^{7} + 70 q^{9} + O(q^{10}) \) \( 2016 q - 672 q^{4} + 56 q^{6} + 12 q^{7} + 70 q^{9} + 132 q^{14} + 168 q^{15} + 2688 q^{16} - 112 q^{18} - 180 q^{21} + 1260 q^{23} + 4200 q^{25} + 84 q^{27} + 96 q^{28} - 210 q^{29} - 56 q^{30} + 560 q^{36} - 1680 q^{37} - 980 q^{39} + 4220 q^{42} - 84 q^{43} - 1904 q^{45} - 2520 q^{46} - 1386 q^{47} + 42 q^{49} + 672 q^{50} - 1092 q^{51} + 672 q^{52} - 4284 q^{55} + 528 q^{56} + 7952 q^{57} + 1260 q^{58} + 1344 q^{60} - 5880 q^{61} + 774 q^{63} + 21504 q^{64} + 4704 q^{65} - 1176 q^{67} - 3640 q^{69} - 216 q^{70} + 448 q^{72} - 2520 q^{74} - 10626 q^{75} - 1500 q^{77} - 224 q^{78} + 588 q^{79} + 6062 q^{81} + 1752 q^{84} + 728 q^{87} + 6972 q^{90} - 180 q^{91} - 2016 q^{92} + 4984 q^{93} + 1764 q^{95} + 39872 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

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