Properties

Label 648.4.d
Level $648$
Weight $4$
Character orbit 648.d
Rep. character $\chi_{648}(325,\cdot)$
Character field $\Q$
Dimension $140$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 336 148 188
Cusp forms 312 140 172
Eisenstein series 24 8 16

Trace form

\( 140q + 2q^{4} + 4q^{7} + O(q^{10}) \) \( 140q + 2q^{4} + 4q^{7} - 20q^{10} + 182q^{16} + 70q^{22} - 3096q^{25} + 376q^{28} + 4q^{31} + 414q^{34} - 68q^{40} + 948q^{46} + 5688q^{49} + 1176q^{52} - 508q^{55} - 1892q^{58} - 958q^{64} + 3656q^{70} - 8q^{73} + 2826q^{76} - 716q^{79} - 474q^{82} - 5522q^{88} + 276q^{94} + 4q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)