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Properties

Label 1800.2.cx
Level $1800$
Weight $2$
Character orbit 1800.cx
Rep. character $\chi_{1800}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2848$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.cx (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1800 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).

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

Trace form

\( 2848 q - 15 q^{2} - 20 q^{3} - 3 q^{4} - 10 q^{6} - 12 q^{9} + O(q^{10}) \) \( 2848 q - 15 q^{2} - 20 q^{3} - 3 q^{4} - 10 q^{6} - 12 q^{9} - 12 q^{10} - 18 q^{11} - 10 q^{12} - 9 q^{14} - 3 q^{16} - 24 q^{19} + 9 q^{20} - 5 q^{22} - 18 q^{24} - 8 q^{25} - 20 q^{27} + 20 q^{28} - 20 q^{33} + q^{34} + 16 q^{36} - 15 q^{38} - 9 q^{40} - 18 q^{41} + 120 q^{42} - 4 q^{46} + 55 q^{48} - 1344 q^{49} + 27 q^{50} - 8 q^{51} - 5 q^{52} - 49 q^{54} + 54 q^{56} - 5 q^{58} - 18 q^{59} - 121 q^{60} - 12 q^{64} - 24 q^{65} + 98 q^{66} - 10 q^{67} - 40 q^{70} - 10 q^{72} - 40 q^{73} + 30 q^{74} - 66 q^{75} + 150 q^{78} - 12 q^{81} - 30 q^{83} - 65 q^{84} - 69 q^{86} - 5 q^{88} + 27 q^{90} + 60 q^{91} - 15 q^{92} + 41 q^{94} + 41 q^{96} - 10 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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