Properties

Label 4000.1.cf
Level $4000$
Weight $1$
Character orbit 4000.cf
Rep. character $\chi_{4000}(159,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $0$
Newform subspaces $0$
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: \(\Q(\zeta_{50})\)
Newform subspaces: \( 0 \)
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

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