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Properties

Label 1800.4.b
Level $1800$
Weight $4$
Character orbit 1800.b
Rep. character $\chi_{1800}(251,\cdot)$
Character field $\Q$
Dimension $228$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1104 228 876
Cusp forms 1056 228 828
Eisenstein series 48 0 48

Trace form

\( 228 q + 12 q^{4} + O(q^{10}) \) \( 228 q + 12 q^{4} - 48 q^{19} - 24 q^{22} + 312 q^{28} - 444 q^{34} + 864 q^{43} - 96 q^{46} - 10452 q^{49} - 384 q^{52} - 2076 q^{58} - 1416 q^{64} + 816 q^{67} - 432 q^{73} - 1032 q^{76} + 84 q^{82} + 1344 q^{88} - 3600 q^{91} - 6336 q^{94} + 3072 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)