Properties

Label 648.4.v
Level $648$
Weight $4$
Character orbit 648.v
Rep. character $\chi_{648}(35,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $636$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.v (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 1980 660 1320
Cusp forms 1908 636 1272
Eisenstein series 72 24 48

Trace form

\( 636q + 6q^{2} - 6q^{4} + 9q^{8} + O(q^{10}) \) \( 636q + 6q^{2} - 6q^{4} + 9q^{8} - 3q^{10} + 12q^{11} + 81q^{14} - 6q^{16} + 18q^{17} - 6q^{19} - 225q^{20} - 6q^{22} - 12q^{25} - 12q^{28} - 684q^{32} - 30q^{34} + 18q^{35} - 888q^{38} + 369q^{40} + 72q^{41} - 12q^{43} + 2673q^{44} - 3q^{46} - 12q^{49} + 3579q^{50} - 1383q^{52} - 4971q^{56} + 885q^{58} + 3072q^{59} - 1872q^{62} - 3q^{64} + 12q^{65} - 12q^{67} + 7209q^{68} - 1059q^{70} - 6q^{73} - 411q^{74} + 186q^{76} - 12q^{82} + 3672q^{83} - 6q^{86} - 1542q^{88} + 18q^{89} - 6q^{91} - 12705q^{92} - 2031q^{94} - 12q^{97} + 2916q^{98} + O(q^{100}) \)

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

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