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Properties

Label 1900.2.cq
Level $1900$
Weight $2$
Character orbit 1900.cq
Rep. character $\chi_{1900}(23,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $14208$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.cq (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1900 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

Total New Old
Modular forms 14592 14592 0
Cusp forms 14208 14208 0
Eisenstein series 384 384 0

Trace form

\( 14208 q - 48 q^{2} - 60 q^{4} - 96 q^{5} - 36 q^{6} - 24 q^{8} - 120 q^{9} + O(q^{10}) \) \( 14208 q - 48 q^{2} - 60 q^{4} - 96 q^{5} - 36 q^{6} - 24 q^{8} - 120 q^{9} - 48 q^{10} - 24 q^{12} - 96 q^{13} - 60 q^{14} - 36 q^{16} - 96 q^{17} - 96 q^{18} - 156 q^{20} - 72 q^{21} - 36 q^{22} - 96 q^{25} - 48 q^{26} - 36 q^{28} - 120 q^{29} - 24 q^{30} - 78 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{36} - 192 q^{37} - 36 q^{38} - 168 q^{40} - 72 q^{41} - 12 q^{42} - 60 q^{44} - 48 q^{45} - 18 q^{46} + 36 q^{48} - 24 q^{50} - 48 q^{52} - 96 q^{53} - 60 q^{54} - 72 q^{56} - 96 q^{57} - 240 q^{58} - 48 q^{60} - 72 q^{61} + 204 q^{62} - 30 q^{64} - 48 q^{65} + 36 q^{66} - 24 q^{68} - 60 q^{69} - 48 q^{70} - 180 q^{72} - 96 q^{73} - 96 q^{76} + 120 q^{77} - 24 q^{78} - 108 q^{80} - 72 q^{81} - 288 q^{82} - 30 q^{84} - 96 q^{85} - 36 q^{86} + 72 q^{88} - 120 q^{89} + 312 q^{90} + 132 q^{92} - 60 q^{93} - 120 q^{94} - 72 q^{96} - 96 q^{97} - 138 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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