Properties

Label 1800.4.cz
Level $1800$
Weight $4$
Character orbit 1800.cz
Rep. character $\chi_{1800}(119,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $0$
Newform subspaces $0$
Sturm bound $1440$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.cz (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 900 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 0 \)
Sturm bound: \(1440\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 8704 0 8704
Cusp forms 8576 0 8576
Eisenstein series 128 0 128

Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)