Properties

Label 729.1.b
Level $729$
Weight $1$
Character orbit 729.b
Rep. character $\chi_{729}(728,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $81$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 729.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(81\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(729, [\chi])\).

Total New Old
Modular forms 20 6 14
Cusp forms 2 0 2
Eisenstein series 18 6 12

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 \(S_{1}^{\mathrm{old}}(729, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(729, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 2}\)