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Properties

Label 882.5.bh
Level $882$
Weight $5$
Character orbit 882.bh
Rep. character $\chi_{882}(13,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2688$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 882.bh (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(882, [\chi])\).

Total New Old
Modular forms 8112 2688 5424
Cusp forms 8016 2688 5328
Eisenstein series 96 0 96

Trace form

\( 2688 q + 1792 q^{4} - 448 q^{6} - 26 q^{7} - 80 q^{9} + O(q^{10}) \) \( 2688 q + 1792 q^{4} - 448 q^{6} - 26 q^{7} - 80 q^{9} + 96 q^{14} + 348 q^{15} + 14336 q^{16} + 512 q^{18} - 234 q^{21} - 3330 q^{23} - 28000 q^{25} - 6090 q^{27} + 416 q^{28} - 1320 q^{29} - 2624 q^{30} + 3732 q^{35} + 1280 q^{36} - 10340 q^{37} + 12376 q^{39} - 7168 q^{42} + 704 q^{43} + 3514 q^{45} - 10560 q^{46} + 14616 q^{47} + 122 q^{49} + 6144 q^{50} + 4776 q^{51} + 560 q^{52} + 52296 q^{53} - 17808 q^{55} + 768 q^{56} + 51560 q^{57} - 12000 q^{58} - 5568 q^{60} + 11858 q^{61} - 3066 q^{63} - 229376 q^{64} + 10164 q^{65} - 15260 q^{67} + 15008 q^{69} - 6048 q^{70} + 54348 q^{71} + 4096 q^{72} + 576 q^{74} + 82992 q^{75} - 30282 q^{77} + 11776 q^{78} + 1948 q^{79} + 5000 q^{81} + 149940 q^{83} - 24528 q^{84} - 21888 q^{86} - 41440 q^{87} - 98700 q^{89} + 51072 q^{90} + 14052 q^{91} + 10656 q^{92} + 45682 q^{93} + 69408 q^{95} + 254208 q^{98} + 42380 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)