Properties

Label 1020.1.cs
Level $1020$
Weight $1$
Character orbit 1020.cs
Rep. character $\chi_{1020}(163,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $0$
Newform subspaces $0$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1020.cs (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 340 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 0 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1020, [\chi])\).

Total New Old
Modular forms 80 0 80
Cusp forms 16 0 16
Eisenstein series 64 0 64

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 \(S_{1}^{\mathrm{old}}(1020, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1020, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 2}\)