Properties

Label 648.4.l
Level $648$
Weight $4$
Character orbit 648.l
Rep. character $\chi_{648}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $284$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 672 292 380
Cusp forms 624 284 340
Eisenstein series 48 8 40

Trace form

\( 284q + 2q^{4} + O(q^{10}) \) \( 284q + 2q^{4} - 36q^{10} + 2q^{16} - 8q^{19} - 14q^{22} - 3346q^{25} + 252q^{28} - 1004q^{34} - 198q^{40} + 4q^{43} - 216q^{46} + 6374q^{49} - 1044q^{52} + 612q^{58} + 3956q^{64} + 4q^{67} - 450q^{70} - 8q^{73} + 2920q^{76} - 1376q^{82} - 6242q^{88} + 2736q^{91} + 2808q^{94} + 4q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)