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Properties

Label 1800.2.dr
Level $1800$
Weight $2$
Character orbit 1800.dr
Rep. character $\chi_{1800}(67,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $5696$
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.dr (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1800 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 5824 5824 0
Cusp forms 5696 5696 0
Eisenstein series 128 128 0

Trace form

\( 5696 q - 8 q^{2} - 32 q^{3} - 10 q^{4} - 12 q^{6} - 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 5696 q - 8 q^{2} - 32 q^{3} - 10 q^{4} - 12 q^{6} - 32 q^{8} - 40 q^{9} - 32 q^{10} - 12 q^{11} - 10 q^{12} - 10 q^{14} - 6 q^{16} - 64 q^{17} - 40 q^{18} - 80 q^{19} - 24 q^{20} - 16 q^{22} - 16 q^{25} - 64 q^{26} - 32 q^{27} - 48 q^{28} + 14 q^{30} + 12 q^{32} - 44 q^{33} - 10 q^{34} - 64 q^{35} + 4 q^{36} + 16 q^{38} - 8 q^{40} - 12 q^{41} - 154 q^{42} - 16 q^{43} - 40 q^{44} - 24 q^{46} - 112 q^{48} + 32 q^{50} - 64 q^{51} - 24 q^{52} + 110 q^{54} - 6 q^{56} - 56 q^{57} - 16 q^{58} - 20 q^{59} + 166 q^{60} + 36 q^{62} - 40 q^{64} - 16 q^{65} - 36 q^{66} - 16 q^{67} + 36 q^{68} - 28 q^{70} - 58 q^{72} - 64 q^{73} + 80 q^{75} - 32 q^{76} - 42 q^{78} - 132 q^{80} - 24 q^{81} - 40 q^{82} - 16 q^{83} - 20 q^{84} - 6 q^{86} + 32 q^{88} - 80 q^{89} - 6 q^{90} - 48 q^{91} - 62 q^{92} - 130 q^{94} - 12 q^{96} - 16 q^{97} + 60 q^{98} + O(q^{100}) \)

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.