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Properties

Label 1900.2.bw
Level $1900$
Weight $2$
Character orbit 1900.bw
Rep. character $\chi_{1900}(179,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2368$
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.bw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1900 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 2432 2432 0
Cusp forms 2368 2368 0
Eisenstein series 64 64 0

Trace form

\( 2368 q - 15 q^{2} - 3 q^{4} - 8 q^{5} + 5 q^{6} - 294 q^{9} + O(q^{10}) \) \( 2368 q - 15 q^{2} - 3 q^{4} - 8 q^{5} + 5 q^{6} - 294 q^{9} - 21 q^{10} - 30 q^{13} - 9 q^{14} - 3 q^{16} - 10 q^{17} - 64 q^{20} - 72 q^{21} - 15 q^{22} - 8 q^{25} - 20 q^{26} - 25 q^{28} - 18 q^{29} + 12 q^{30} - 30 q^{33} - 9 q^{34} - 25 q^{36} - 5 q^{38} + 84 q^{40} - 18 q^{41} - 35 q^{42} - 53 q^{44} - 40 q^{45} - 15 q^{48} + 2112 q^{49} - 15 q^{52} - 30 q^{53} - 22 q^{54} + 150 q^{58} + 96 q^{60} - 6 q^{61} - 30 q^{62} + 54 q^{64} - 11 q^{66} - 132 q^{70} + 210 q^{72} - 10 q^{73} - 18 q^{74} + 32 q^{76} - 320 q^{77} + 30 q^{78} - 17 q^{80} + 198 q^{81} + 16 q^{85} - 99 q^{86} - 18 q^{89} + 111 q^{90} - 55 q^{92} - 10 q^{96} - 30 q^{97} - 150 q^{98} + O(q^{100}) \)

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.