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Properties

Label 1800.4.bg
Level $1800$
Weight $4$
Character orbit 1800.bg
Rep. character $\chi_{1800}(301,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1356$
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.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2184 1380 804
Cusp forms 2136 1356 780
Eisenstein series 48 24 24

Trace form

\( 1356 q + q^{2} + q^{4} - 13 q^{6} + 2 q^{7} - 2 q^{8} + 4 q^{9} + O(q^{10}) \) \( 1356 q + q^{2} + q^{4} - 13 q^{6} + 2 q^{7} - 2 q^{8} + 4 q^{9} + 6 q^{12} + 24 q^{14} - 3 q^{16} + 8 q^{17} + 174 q^{18} + 17 q^{22} + 278 q^{23} + 105 q^{24} + 936 q^{26} - 124 q^{28} - 6 q^{31} + 721 q^{32} + 290 q^{33} - 221 q^{34} - 45 q^{36} - 899 q^{38} + 142 q^{39} - 26 q^{41} - 828 q^{42} - 1822 q^{44} + 8 q^{46} - 938 q^{47} + 1381 q^{48} - 31456 q^{49} - 330 q^{52} - 1977 q^{54} + 1498 q^{56} - 276 q^{57} + 314 q^{58} - 1460 q^{62} - 642 q^{63} - 950 q^{64} + 940 q^{66} + 1955 q^{68} + 3952 q^{71} + 4401 q^{72} + 8 q^{73} + 74 q^{74} - 369 q^{76} + 1720 q^{78} + 2 q^{79} - 168 q^{81} + 690 q^{82} - 5402 q^{84} + 2659 q^{86} + 4758 q^{87} + 533 q^{88} + 856 q^{89} - 66 q^{92} - 104 q^{94} - 5302 q^{96} + 2 q^{97} - 5226 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)