Properties

Label 712.1.v
Level $712$
Weight $1$
Character orbit 712.v
Rep. character $\chi_{712}(39,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $0$
Newform subspaces $0$
Sturm bound $90$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 712 = 2^{3} \cdot 89 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 712.v (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 356 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 0 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(712, [\chi])\).

Total New Old
Modular forms 60 0 60
Cusp forms 20 0 20
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

Decomposition of \(S_{1}^{\mathrm{old}}(712, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(712, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(356, [\chi])\)\(^{\oplus 2}\)