Properties

Label 136.3.l
Level $136$
Weight $3$
Character orbit 136.l
Rep. character $\chi_{136}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $0$
Newform subspaces $0$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(136, [\chi])\).

Total New Old
Modular forms 80 0 80
Cusp forms 64 0 64
Eisenstein series 16 0 16

Decomposition of \(S_{3}^{\mathrm{old}}(136, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(136, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)