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Properties

Label 882.5.be
Level $882$
Weight $5$
Character orbit 882.be
Rep. character $\chi_{882}(11,\cdot)$
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.be (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

\( 2688 q + 3584 q^{4} - 160 q^{6} + 26 q^{7} + 80 q^{9} + O(q^{10}) \) \( 2688 q + 3584 q^{4} - 160 q^{6} + 26 q^{7} + 80 q^{9} + 10 q^{13} - 288 q^{14} + 174 q^{15} - 28672 q^{16} - 1350 q^{17} + 512 q^{18} - 308 q^{19} - 352 q^{21} - 1998 q^{23} - 512 q^{24} - 28000 q^{25} - 1152 q^{26} + 10290 q^{27} - 208 q^{28} + 792 q^{29} + 256 q^{30} + 736 q^{31} - 2600 q^{33} - 5490 q^{35} - 640 q^{36} + 13442 q^{37} - 3538 q^{39} - 4464 q^{41} + 1792 q^{42} + 352 q^{43} - 63776 q^{45} + 13728 q^{46} - 43848 q^{47} - 3814 q^{49} - 9216 q^{50} + 1014 q^{51} + 1040 q^{52} + 5472 q^{53} + 7744 q^{54} + 6360 q^{55} + 2304 q^{56} - 23520 q^{57} + 31200 q^{58} - 1392 q^{60} - 2902 q^{61} + 12270 q^{63} + 229376 q^{64} - 8576 q^{66} - 15260 q^{67} + 10800 q^{68} + 15954 q^{69} + 1152 q^{70} - 156870 q^{71} - 4096 q^{72} + 19012 q^{73} + 864 q^{74} + 112490 q^{75} + 2464 q^{76} + 10206 q^{77} - 5888 q^{78} + 15868 q^{79} - 44200 q^{81} + 31376 q^{84} + 25068 q^{87} - 132012 q^{89} + 87040 q^{90} - 11762 q^{91} + 15984 q^{92} - 142184 q^{93} + 2688 q^{94} + 4096 q^{96} + 6346 q^{97} + 14976 q^{98} + 54458 q^{99} + O(q^{100}) \)

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

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