Properties

Label 1176.1.bt
Level $1176$
Weight $1$
Character orbit 1176.bt
Rep. character $\chi_{1176}(113,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $0$
Newform subspaces $0$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1176.bt (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 0 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1176, [\chi])\).

Total New Old
Modular forms 72 0 72
Cusp forms 24 0 24
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 \(S_{1}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)