Properties

Label 136.4.r
Level $136$
Weight $4$
Character orbit 136.r
Rep. character $\chi_{136}(7,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $0$
Newform subspaces $0$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 136.r (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 0 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(136, [\chi])\).

Total New Old
Modular forms 464 0 464
Cusp forms 400 0 400
Eisenstein series 64 0 64

Decomposition of \(S_{4}^{\mathrm{old}}(136, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(136, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)