Properties

Label 448.1.v
Level $448$
Weight $1$
Character orbit 448.v
Rep. character $\chi_{448}(41,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $0$
Newform subspaces $0$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 448.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 0 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(448, [\chi])\).

Total New Old
Modular forms 24 0 24
Cusp forms 8 0 8
Eisenstein series 16 0 16

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 \(S_{1}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)