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Properties

Label 900.3.bl
Level $900$
Weight $3$
Character orbit 900.bl
Rep. character $\chi_{900}(79,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2848$
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.bl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 900 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 2912 2912 0
Cusp forms 2848 2848 0
Eisenstein series 64 64 0

Trace form

\( 2848 q - 5 q^{2} - 3 q^{4} - 8 q^{5} - 14 q^{6} - 20 q^{8} - 12 q^{9} + O(q^{10}) \) \( 2848 q - 5 q^{2} - 3 q^{4} - 8 q^{5} - 14 q^{6} - 20 q^{8} - 12 q^{9} - 8 q^{10} - 10 q^{12} - 10 q^{13} + 21 q^{14} - 3 q^{16} - 40 q^{17} - 15 q^{20} + 42 q^{21} - 5 q^{22} - 50 q^{24} - 8 q^{25} - 16 q^{26} + 140 q^{28} - 6 q^{29} + 40 q^{30} - 20 q^{33} - 11 q^{34} - 188 q^{36} - 40 q^{37} + 625 q^{38} - 29 q^{40} - 6 q^{41} - 530 q^{42} + 52 q^{44} - 90 q^{45} - 28 q^{46} + 55 q^{48} - 9312 q^{49} + 145 q^{50} - 5 q^{52} - 40 q^{53} - 209 q^{54} - 150 q^{56} - 5 q^{58} + 707 q^{60} - 6 q^{61} - 20 q^{62} - 12 q^{64} + 44 q^{65} - 394 q^{66} + 192 q^{69} - 246 q^{70} - 10 q^{72} - 40 q^{73} + 194 q^{74} - 40 q^{76} + 970 q^{77} + 1510 q^{78} + 930 q^{80} + 468 q^{81} + 525 q^{84} - 58 q^{85} - 279 q^{86} - 5 q^{88} - 24 q^{89} + 57 q^{90} - 5 q^{92} - 199 q^{94} + 211 q^{96} - 10 q^{97} + 510 q^{98} + O(q^{100}) \)

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.