Properties

Label 1764.1.bk
Level $1764$
Weight $1$
Character orbit 1764.bk
Rep. character $\chi_{1764}(557,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $0$
Newform subspaces $0$
Sturm bound $336$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1764.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 0 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1764, [\chi])\).

Total New Old
Modular forms 120 0 120
Cusp forms 24 0 24
Eisenstein series 96 0 96

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 \(S_{1}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)