Properties

Label 648.4.be
Level $648$
Weight $4$
Character orbit 648.be
Rep. character $\chi_{648}(23,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $0$
Newform subspaces $0$
Sturm bound $432$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.be (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 324 \)
Character field: \(\Q(\zeta_{54})\)
Newform subspaces: \( 0 \)
Sturm bound: \(432\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(648, [\chi])\).

Total New Old
Modular forms 5904 0 5904
Cusp forms 5760 0 5760
Eisenstein series 144 0 144

Decomposition of \(S_{4}^{\mathrm{old}}(648, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)