Properties

Label 648.4.n
Level $648$
Weight $4$
Character orbit 648.n
Rep. character $\chi_{648}(109,\cdot)$
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.n (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

\( 284 q + 2 q^{4} + 4 q^{7} + O(q^{10}) \) \( 284 q + 2 q^{4} + 4 q^{7} + 28 q^{10} + 2 q^{16} - 14 q^{22} + 3354 q^{25} - 260 q^{28} + 4 q^{31} - 972 q^{34} - 698 q^{40} + 144 q^{46} - 6366 q^{49} + 792 q^{52} + 992 q^{55} - 608 q^{58} - 2884 q^{64} + 422 q^{70} - 8 q^{73} - 2916 q^{76} + 4 q^{79} - 1440 q^{82} + 4198 q^{88} - 5472 q^{94} + 4 q^{97} + O(q^{100}) \)

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

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