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Properties

Label 900.3.bu
Level $900$
Weight $3$
Character orbit 900.bu
Rep. character $\chi_{900}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $5696$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.bu (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 900 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 5824 5824 0
Cusp forms 5696 5696 0
Eisenstein series 128 128 0

Trace form

\( 5696 q - 24 q^{2} - 10 q^{4} - 48 q^{5} - 12 q^{6} - 40 q^{9} + O(q^{10}) \) \( 5696 q - 24 q^{2} - 10 q^{4} - 48 q^{5} - 12 q^{6} - 40 q^{9} - 32 q^{10} - 34 q^{12} - 16 q^{13} - 30 q^{14} - 6 q^{16} + 4 q^{18} - 24 q^{20} - 24 q^{21} - 24 q^{22} - 16 q^{25} - 96 q^{28} - 60 q^{29} + 54 q^{30} + 156 q^{32} - 68 q^{33} - 10 q^{34} + 52 q^{36} - 64 q^{37} - 8 q^{40} - 36 q^{41} + 1202 q^{42} - 132 q^{45} - 24 q^{46} + 52 q^{48} - 24 q^{50} + 56 q^{52} + 630 q^{54} - 18 q^{56} + 8 q^{57} - 24 q^{58} - 1838 q^{60} - 12 q^{61} - 40 q^{64} + 240 q^{65} - 156 q^{66} + 72 q^{68} - 40 q^{69} - 108 q^{70} - 230 q^{72} - 64 q^{73} + 48 q^{76} - 48 q^{77} + 310 q^{78} - 24 q^{81} - 16 q^{82} - 20 q^{84} - 16 q^{85} - 18 q^{86} + 96 q^{88} - 86 q^{90} - 366 q^{92} - 668 q^{93} + 590 q^{94} - 12 q^{96} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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