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Properties

Label 1800.2.df
Level $1800$
Weight $2$
Character orbit 1800.df
Rep. character $\chi_{1800}(229,\cdot)$
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.df (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

\( 2848 q - 5 q^{2} - 3 q^{4} - 10 q^{6} - 20 q^{8} - 12 q^{9} + O(q^{10}) \) \( 2848 q - 5 q^{2} - 3 q^{4} - 10 q^{6} - 20 q^{8} - 12 q^{9} - 20 q^{10} - 10 q^{12} - 15 q^{14} - 22 q^{15} - 3 q^{16} - 40 q^{17} - 3 q^{20} - 5 q^{22} - 10 q^{23} + 10 q^{24} - 8 q^{25} - 40 q^{26} - 60 q^{28} + 2 q^{30} - 6 q^{31} - 20 q^{33} - 7 q^{34} - 44 q^{36} - 75 q^{38} - 24 q^{39} + q^{40} - 6 q^{41} + 60 q^{42} + 4 q^{44} - 4 q^{46} - 10 q^{47} + 55 q^{48} + 1312 q^{49} + 7 q^{50} - 5 q^{52} - 49 q^{54} - 12 q^{55} + 18 q^{56} - 5 q^{58} - 87 q^{60} - 20 q^{62} - 90 q^{63} - 12 q^{64} - 28 q^{65} + 94 q^{66} + 36 q^{70} + 88 q^{71} - 10 q^{72} - 40 q^{73} - 18 q^{74} - 16 q^{76} - 110 q^{78} - 6 q^{79} + 206 q^{80} - 12 q^{81} + 69 q^{84} - 11 q^{86} - 20 q^{87} - 5 q^{88} - 24 q^{89} - 17 q^{90} - 5 q^{92} - 31 q^{94} - 18 q^{95} - 35 q^{96} - 10 q^{97} - 70 q^{98} + O(q^{100}) \)

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.