↑

Properties

Label 1900.2.cj
Level $1900$
Weight $2$
Character orbit 1900.cj
Rep. character $\chi_{1900}(59,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $7104$
Sturm bound $600$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.cj (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1900 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 7296 7296 0
Cusp forms 7104 7104 0
Eisenstein series 192 192 0

Trace form

\( 7104 q - 30 q^{2} - 18 q^{4} - 48 q^{5} - 18 q^{6} - 45 q^{8} - 36 q^{9} + O(q^{10}) \) \( 7104 q - 30 q^{2} - 18 q^{4} - 48 q^{5} - 18 q^{6} - 45 q^{8} - 36 q^{9} - 15 q^{10} - 45 q^{12} - 60 q^{13} - 18 q^{14} - 18 q^{16} - 60 q^{17} - 18 q^{20} + 18 q^{21} - 30 q^{22} - 72 q^{24} - 48 q^{25} - 24 q^{26} + 30 q^{28} - 36 q^{29} + 9 q^{30} - 60 q^{33} - 18 q^{34} + 15 q^{38} - 57 q^{40} - 36 q^{41} + 60 q^{42} + 6 q^{44} - 24 q^{45} - 27 q^{46} - 30 q^{48} - 3312 q^{49} - 9 q^{50} - 30 q^{52} - 60 q^{53} + 48 q^{54} - 420 q^{58} - 105 q^{60} - 36 q^{61} - 180 q^{62} - 9 q^{64} - 72 q^{65} + 18 q^{66} - 54 q^{69} + 96 q^{70} + 420 q^{72} - 60 q^{73} + 18 q^{74} - 48 q^{76} + 300 q^{77} - 75 q^{78} - 33 q^{80} - 27 q^{84} - 24 q^{85} + 72 q^{86} - 45 q^{88} - 36 q^{89} - 327 q^{90} + 120 q^{92} - 36 q^{96} - 60 q^{97} + 105 q^{98} + O(q^{100}) \)

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.