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Properties

Label 900.6.bn
Level $900$
Weight $6$
Character orbit 900.bn
Rep. character $\chi_{900}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $7168$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.bn (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

\( 7168 q - 15 q^{2} - 3 q^{4} - 24 q^{5} + 58 q^{6} - 12 q^{9} + O(q^{10}) \) \( 7168 q - 15 q^{2} - 3 q^{4} - 24 q^{5} + 58 q^{6} - 12 q^{9} - 80 q^{10} - 10 q^{12} - 10 q^{13} - 9 q^{14} - 3 q^{16} - 1251 q^{20} + 1446 q^{21} - 5 q^{22} - 9374 q^{24} - 8 q^{25} + 10220 q^{28} - 18 q^{29} + 3982 q^{30} - 20 q^{33} + 61 q^{34} - 25424 q^{36} - 40 q^{37} - 15 q^{38} + 3121 q^{40} - 18 q^{41} + 239770 q^{42} + 24246 q^{45} + 116 q^{46} + 140455 q^{48} - 8374704 q^{49} + 47997 q^{50} - 5 q^{52} - 19793 q^{54} + 151254 q^{56} - 5 q^{58} + 107897 q^{60} - 6 q^{61} - 12 q^{64} - 36000 q^{65} - 13318 q^{66} - 141576 q^{69} - 61014 q^{70} - 10 q^{72} - 40 q^{73} - 258558 q^{74} - 2056 q^{76} - 30 q^{77} + 984130 q^{78} - 371484 q^{81} - 55617 q^{84} + 6242 q^{85} + 1731 q^{86} - 5 q^{88} - 441483 q^{90} - 15 q^{92} - 86671 q^{94} - 101093 q^{96} - 10 q^{97} + O(q^{100}) \)

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.