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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

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

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

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