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Properties

Label 648.4.f
Level $648$
Weight $4$
Character orbit 648.f
Rep. character $\chi_{648}(323,\cdot)$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
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

\( 140 q + 2 q^{4} + O(q^{10}) \) \( 140 q + 2 q^{4} + 12 q^{10} - 178 q^{16} - 8 q^{19} - 2 q^{22} + 3104 q^{25} + 120 q^{28} + 382 q^{34} + 432 q^{40} + 4 q^{43} + 876 q^{46} - 5680 q^{49} - 660 q^{52} - 768 q^{58} + 410 q^{64} - 2444 q^{67} + 1284 q^{70} - 8 q^{73} + 850 q^{76} + 1870 q^{82} - 1346 q^{88} - 1380 q^{91} - 3036 q^{94} + 4 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)