Properties

Label 400.1.z
Level 400
Weight 1
Character orbit z
Rep. character \(\chi_{400}(31,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 0
Newform subspaces 0
Sturm bound 60
Trace bound 0

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Defining parameters

Level: \( N \) = \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 400.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 0 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(400, [\chi])\).

Total New Old
Modular forms 36 0 36
Cusp forms 12 0 12
Eisenstein series 24 0 24

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 \(S_{1}^{\mathrm{old}}(400, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)