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Properties

Label 1800.4.bl
Level $1800$
Weight $4$
Character orbit 1800.bl
Rep. character $\chi_{1800}(349,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1288$
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.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
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 1304 880
Cusp forms 2136 1288 848
Eisenstein series 48 16 32

Trace form

\( 1288 q + 2 q^{4} - 20 q^{6} + 8 q^{9} + O(q^{10}) \) \( 1288 q + 2 q^{4} - 20 q^{6} + 8 q^{9} - 30 q^{14} - 2 q^{16} - 458 q^{24} + 504 q^{26} - 4 q^{31} + 414 q^{34} + 112 q^{36} + 116 q^{39} - 4 q^{41} + 2632 q^{44} + 96 q^{46} + 30384 q^{49} + 1162 q^{54} + 628 q^{56} + 1376 q^{64} + 4806 q^{66} - 7968 q^{71} - 2520 q^{74} - 990 q^{76} + 4 q^{79} - 1240 q^{81} - 1122 q^{84} - 42 q^{86} - 1680 q^{89} - 1686 q^{94} - 1788 q^{96} + O(q^{100}) \)

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

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