Properties

Label 1800.1.cn
Level 1800
Weight 1
Character orbit cn
Rep. character \(\chi_{1800}(287,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 0
Newforms 0
Sturm bound 360
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1800.cn (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 300 \)
Character field: \(\Q(\zeta_{20})\)
Newforms: \( 0 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).

Total New Old
Modular forms 160 0 160
Cusp forms 32 0 32
Eisenstein series 128 0 128

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 0 0

Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)