Properties

Label 4000.1.cf
Level 4000
Weight 1
Character orbit cf
Rep. character \(\chi_{4000}(159,\cdot)\)
Character field \(\Q(\zeta_{50})\)
Dimension 0
Newforms 0
Sturm bound 600
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4000 = 2^{5} \cdot 5^{3} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 4000.cf (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 500 \)
Character field: \(\Q(\zeta_{50})\)
Newforms: \( 0 \)
Sturm bound: \(600\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(4000, [\chi])\).

Total New Old
Modular forms 200 0 200
Cusp forms 40 0 40
Eisenstein series 160 0 160

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 \(S_{1}^{\mathrm{old}}(4000, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)