Properties

Label 4000.1.z
Level 4000
Weight 1
Character orbit z
Rep. character \(\chi_{4000}(499,\cdot)\)
Character field \(\Q(\zeta_{8})\)
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.z (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 160 \)
Character field: \(\Q(\zeta_{8})\)
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 40 0 40
Cusp forms 0 0 0
Eisenstein series 40 0 40

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