Properties

Label 1400.1.be
Level $1400$
Weight $1$
Character orbit 1400.be
Rep. character $\chi_{1400}(599,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $0$
Newform subspaces $0$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1400.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 0 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1400, [\chi])\).

Total New Old
Modular forms 64 0 64
Cusp forms 16 0 16
Eisenstein series 48 0 48

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 \(S_{1}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)