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Properties

Label 1800.2.cv
Level $1800$
Weight $2$
Character orbit 1800.cv
Rep. character $\chi_{1800}(61,\cdot)$
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.cv (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

\( 2848 q - 3 q^{2} - 3 q^{4} - 2 q^{6} - 16 q^{7} - 12 q^{8} - 12 q^{9} + O(q^{10}) \) \( 2848 q - 3 q^{2} - 3 q^{4} - 2 q^{6} - 16 q^{7} - 12 q^{8} - 12 q^{9} - 12 q^{10} + 9 q^{14} - 10 q^{15} - 3 q^{16} - 24 q^{17} - 48 q^{18} + 11 q^{20} + 5 q^{22} - 6 q^{23} - 14 q^{24} - 8 q^{25} - 24 q^{26} + 12 q^{28} - 28 q^{30} - 6 q^{31} - 28 q^{32} + q^{34} + 16 q^{36} + 35 q^{38} - 9 q^{40} - 6 q^{41} + 82 q^{42} + 4 q^{44} - 20 q^{46} - 6 q^{47} + 53 q^{48} - 1344 q^{49} + 25 q^{50} + 13 q^{52} - 41 q^{54} - 12 q^{55} - 24 q^{56} - 56 q^{57} + 5 q^{58} - 67 q^{60} + 40 q^{62} + 30 q^{63} - 12 q^{64} + 12 q^{65} - 82 q^{66} + 52 q^{68} - 24 q^{70} - 136 q^{71} + 16 q^{72} - 24 q^{73} - 26 q^{74} - 16 q^{76} + 60 q^{78} - 6 q^{79} - 98 q^{80} - 12 q^{81} - 40 q^{82} + 87 q^{84} + 5 q^{86} - 56 q^{87} - 43 q^{88} - 24 q^{89} - 69 q^{90} + 19 q^{92} - 47 q^{94} - 18 q^{95} + 23 q^{96} - 6 q^{97} - 110 q^{98} + O(q^{100}) \)

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.