Properties

Label 1407.1.cw
Level $1407$
Weight $1$
Character orbit 1407.cw
Rep. character $\chi_{1407}(55,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $0$
Newform subspaces $0$
Sturm bound $181$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1407 = 3 \cdot 7 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1407.cw (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 469 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 0 \)
Sturm bound: \(181\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1407, [\chi])\).

Total New Old
Modular forms 120 0 120
Cusp forms 40 0 40
Eisenstein series 80 0 80

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 \(S_{1}^{\mathrm{old}}(1407, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1407, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(469, [\chi])\)\(^{\oplus 2}\)