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Properties

Label 1800.4.bw
Level $1800$
Weight $4$
Character orbit 1800.bw
Rep. character $\chi_{1800}(611,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1440$
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.bw (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 600 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4352 1440 2912
Cusp forms 4288 1440 2848
Eisenstein series 64 0 64

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q - 72 q^{10} - 216 q^{16} + 432 q^{22} + 864 q^{28} - 288 q^{34} - 1572 q^{40} + 1728 q^{43} + 840 q^{46} - 70560 q^{49} + 2052 q^{52} + 2088 q^{58} - 1872 q^{64} + 2928 q^{70} + 1224 q^{76} + 10560 q^{82} + 984 q^{88} + 204 q^{94} - 4464 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)