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Properties

Label 1800.4.ce
Level $1800$
Weight $4$
Character orbit 1800.ce
Rep. character $\chi_{1800}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2576$
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.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4368 2608 1760
Cusp forms 4272 2576 1696
Eisenstein series 96 32 64

Trace form

\( 2576 q + 2 q^{2} + 8 q^{3} - 8 q^{6} + 8 q^{8} + O(q^{10}) \) \( 2576 q + 2 q^{2} + 8 q^{3} - 8 q^{6} + 8 q^{8} - 8 q^{11} + 58 q^{12} - 4 q^{16} + 16 q^{17} + 496 q^{18} - 30 q^{22} - 1104 q^{26} + 8 q^{27} - 248 q^{28} - 458 q^{32} - 100 q^{33} - 680 q^{36} + 1190 q^{38} - 8 q^{41} + 786 q^{42} + 4 q^{43} + 128 q^{46} - 250 q^{48} - 16 q^{51} - 254 q^{52} + 2628 q^{56} - 208 q^{57} - 30 q^{58} - 3140 q^{62} + 6496 q^{66} + 4 q^{67} + 550 q^{68} + 586 q^{72} + 16 q^{73} + 2484 q^{76} + 5690 q^{78} - 2480 q^{81} - 24 q^{82} + 4 q^{83} - 5548 q^{86} - 1062 q^{88} - 32 q^{91} + 2900 q^{92} - 3504 q^{96} + 4 q^{97} - 3916 q^{98} + O(q^{100}) \)

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

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