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Properties

Label 1800.2.dd
Level $1800$
Weight $2$
Character orbit 1800.dd
Rep. character $\chi_{1800}(11,\cdot)$
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.dd (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

\( 2848 q - 9 q^{2} - 12 q^{3} - 3 q^{4} - 2 q^{6} - 12 q^{9} + O(q^{10}) \) \( 2848 q - 9 q^{2} - 12 q^{3} - 3 q^{4} - 2 q^{6} - 12 q^{9} - 20 q^{10} - 18 q^{11} - 12 q^{12} - 9 q^{14} - 3 q^{16} + 16 q^{18} - 24 q^{19} - 33 q^{20} + 5 q^{22} - 42 q^{24} - 8 q^{25} - 12 q^{27} - 36 q^{28} - 6 q^{30} - 84 q^{32} - 7 q^{34} - 44 q^{36} + 3 q^{38} + q^{40} - 18 q^{41} + 38 q^{42} - 16 q^{43} - 20 q^{46} + 41 q^{48} + 1312 q^{49} - 51 q^{50} - 56 q^{51} + 13 q^{52} - 41 q^{54} - 72 q^{56} - 8 q^{57} - 11 q^{58} - 18 q^{59} - 17 q^{60} - 12 q^{64} - 24 q^{65} - 86 q^{66} - 6 q^{67} - 48 q^{68} + 12 q^{70} + 12 q^{72} - 24 q^{73} + 6 q^{74} - 78 q^{75} - 20 q^{78} - 12 q^{81} - 24 q^{82} - 18 q^{83} - 83 q^{84} + 51 q^{86} + 5 q^{88} + 99 q^{90} - 108 q^{91} - 123 q^{92} + 25 q^{94} - 53 q^{96} - 6 q^{97} + 4 q^{99} + O(q^{100}) \)

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.