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Properties

Label 1900.3.cr
Level $1900$
Weight $3$
Character orbit 1900.cr
Rep. character $\chi_{1900}(3,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $28608$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.cr (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1900 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

Total New Old
Modular forms 28992 28992 0
Cusp forms 28608 28608 0
Eisenstein series 384 384 0

Trace form

\( 28608 q - 48 q^{2} - 60 q^{4} - 96 q^{5} - 36 q^{6} - 72 q^{8} - 120 q^{9} + O(q^{10}) \) \( 28608 q - 48 q^{2} - 60 q^{4} - 96 q^{5} - 36 q^{6} - 72 q^{8} - 120 q^{9} - 48 q^{10} - 72 q^{12} - 96 q^{13} - 60 q^{14} - 36 q^{16} - 96 q^{17} - 36 q^{20} - 72 q^{21} - 24 q^{22} - 96 q^{25} - 48 q^{26} - 468 q^{28} - 120 q^{29} - 24 q^{30} - 258 q^{32} + 12 q^{33} - 60 q^{34} - 36 q^{36} - 756 q^{38} + 1032 q^{40} - 72 q^{41} + 168 q^{42} - 60 q^{44} - 48 q^{45} - 54 q^{46} + 876 q^{48} - 72 q^{50} - 48 q^{52} - 96 q^{53} - 60 q^{54} - 96 q^{57} + 48 q^{58} - 48 q^{60} - 72 q^{61} - 3192 q^{62} - 30 q^{64} - 144 q^{65} + 396 q^{66} - 24 q^{68} - 180 q^{69} - 48 q^{70} + 108 q^{72} - 96 q^{73} - 96 q^{76} + 1272 q^{77} - 864 q^{78} - 108 q^{80} - 72 q^{81} - 1128 q^{82} - 90 q^{84} - 96 q^{85} - 36 q^{86} - 72 q^{88} - 120 q^{89} + 3192 q^{90} - 2748 q^{92} - 204 q^{93} - 72 q^{96} - 96 q^{97} - 438 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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