Properties

Label 156.1.g
Level $156$
Weight $1$
Character orbit 156.g
Rep. character $\chi_{156}(77,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 156.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(156, [\chi])\).

Total New Old
Modular forms 9 0 9
Cusp forms 3 0 3
Eisenstein series 6 0 6

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 \(S_{1}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)