↑

Properties

Label 900.6.br
Level $900$
Weight $6$
Character orbit 900.br
Rep. character $\chi_{900}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $7168$
Sturm bound $1080$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 900 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(900, [\chi])\).

Total New Old
Modular forms 7232 7232 0
Cusp forms 7168 7168 0
Eisenstein series 64 64 0

Trace form

\( 7168 q - 9 q^{2} - 3 q^{4} - 24 q^{5} - 70 q^{6} - 12 q^{9} + O(q^{10}) \) \( 7168 q - 9 q^{2} - 3 q^{4} - 24 q^{5} - 70 q^{6} - 12 q^{9} + 48 q^{10} + 480 q^{12} - 6 q^{13} - 9 q^{14} - 3 q^{16} - 7540 q^{18} + 1227 q^{20} - 1470 q^{21} - 131 q^{22} - 7430 q^{24} - 8 q^{25} - 6156 q^{28} - 18 q^{29} + 18472 q^{30} + 14436 q^{32} - 984 q^{33} - 67 q^{34} + 21316 q^{36} - 24 q^{37} - 201 q^{38} - 3129 q^{40} - 18 q^{41} + 96784 q^{42} - 11778 q^{45} - 140 q^{46} + 91465 q^{48} + 8374672 q^{49} - 48021 q^{50} - 4099 q^{52} - 19921 q^{54} - 151272 q^{56} + 39320 q^{57} + 125 q^{58} + 357745 q^{60} - 6 q^{61} - 12 q^{64} - 36000 q^{65} - 17798 q^{66} - 6168 q^{68} - 143520 q^{69} + 73506 q^{70} - 165868 q^{72} - 24 q^{73} - 258174 q^{74} - 2056 q^{76} - 18 q^{77} - 386684 q^{78} + 371460 q^{81} + 96 q^{82} - 158403 q^{84} - 6258 q^{85} - 1749 q^{86} + 245077 q^{88} - 215363 q^{90} - 690963 q^{92} + 366652 q^{93} - 86927 q^{94} + 101081 q^{96} - 6 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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