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Properties

Label 648.4.q
Level $648$
Weight $4$
Character orbit 648.q
Rep. character $\chi_{648}(73,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $162$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.q (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 2016 162 1854
Cusp forms 1872 162 1710
Eisenstein series 144 0 144

Trace form

\( 162 q + O(q^{10}) \) \( 162 q - 75 q^{11} + 204 q^{17} - 156 q^{23} + 126 q^{29} - 1260 q^{35} + 1191 q^{41} + 513 q^{43} + 1350 q^{47} - 594 q^{49} - 1908 q^{53} - 966 q^{59} + 54 q^{61} + 1800 q^{65} + 1161 q^{67} - 3084 q^{77} + 1410 q^{83} + 1089 q^{89} - 3522 q^{95} - 81 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(648, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{4}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)