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Properties

Label 1800.4.ch
Level $1800$
Weight $4$
Character orbit 1800.ch
Rep. character $\chi_{1800}(293,\cdot)$
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.ch (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

\( 2576 q + 6 q^{2} - 8 q^{6} + 4 q^{7} + O(q^{10}) \) \( 2576 q + 6 q^{2} - 8 q^{6} + 4 q^{7} - 50 q^{12} - 4 q^{16} - 488 q^{18} - 30 q^{22} + 12 q^{23} + 264 q^{28} - 8 q^{31} - 1374 q^{32} - 100 q^{33} + 152 q^{36} + 54 q^{38} - 24 q^{41} - 110 q^{42} - 160 q^{46} + 12 q^{47} - 142 q^{48} - 254 q^{52} - 7908 q^{56} + 224 q^{57} + 34 q^{58} + 1380 q^{63} - 6688 q^{66} + 390 q^{68} + 3302 q^{72} + 16 q^{73} - 2492 q^{76} - 4634 q^{78} + 2448 q^{81} + 40 q^{82} + 16620 q^{86} - 1172 q^{87} + 3114 q^{88} - 9456 q^{92} - 4688 q^{96} + 4 q^{97} + O(q^{100}) \)

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

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