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

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

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

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