Properties

Label 648.4.w
Level $648$
Weight $4$
Character orbit 648.w
Rep. character $\chi_{648}(71,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $0$
Newform subspaces $0$
Sturm bound $432$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.w (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 108 \)
Character field: \(\Q(\zeta_{18})\)
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 2016 0 2016
Cusp forms 1872 0 1872
Eisenstein series 144 0 144

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

\( S_{4}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)