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Properties

Label 1800.4.dr
Level $1800$
Weight $4$
Character orbit 1800.dr
Rep. character $\chi_{1800}(67,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $17216$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.dr (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1800 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).

Total New Old
Modular forms 17344 17344 0
Cusp forms 17216 17216 0
Eisenstein series 128 128 0

Trace form

\( 17216 q - 8 q^{2} - 32 q^{3} - 10 q^{4} - 12 q^{6} - 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 17216 q - 8 q^{2} - 32 q^{3} - 10 q^{4} - 12 q^{6} - 32 q^{8} - 40 q^{9} - 32 q^{10} - 12 q^{11} + 38 q^{12} - 10 q^{14} - 6 q^{16} - 64 q^{17} + 476 q^{18} - 80 q^{19} - 264 q^{20} - 40 q^{22} - 16 q^{25} - 64 q^{26} - 32 q^{27} - 288 q^{28} - 346 q^{30} - 468 q^{32} - 140 q^{33} - 10 q^{34} - 64 q^{35} + 244 q^{36} + 1180 q^{38} - 8 q^{40} - 12 q^{41} - 634 q^{42} - 16 q^{43} - 40 q^{44} - 24 q^{46} + 5840 q^{48} + 1232 q^{50} - 64 q^{51} - 264 q^{52} - 3790 q^{54} - 6 q^{56} - 248 q^{57} - 40 q^{58} - 20 q^{59} + 7846 q^{60} - 3180 q^{62} - 40 q^{64} - 16 q^{65} - 876 q^{66} - 16 q^{67} + 540 q^{68} - 508 q^{70} + 566 q^{72} - 64 q^{73} - 6640 q^{75} - 272 q^{76} + 5130 q^{78} + 348 q^{80} - 24 q^{81} - 64 q^{82} - 16 q^{83} - 20 q^{84} - 6 q^{86} - 1072 q^{88} - 80 q^{89} - 10626 q^{90} - 48 q^{91} + 2890 q^{92} + 8270 q^{94} - 12 q^{96} - 16 q^{97} - 4116 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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