Properties

Label 648.4.n
Level $648$
Weight $4$
Character orbit 648.n
Rep. character $\chi_{648}(109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $284$
Sturm bound $432$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.n (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

\( 284q + 2q^{4} + 4q^{7} + O(q^{10}) \) \( 284q + 2q^{4} + 4q^{7} + 28q^{10} + 2q^{16} - 14q^{22} + 3354q^{25} - 260q^{28} + 4q^{31} - 972q^{34} - 698q^{40} + 144q^{46} - 6366q^{49} + 792q^{52} + 992q^{55} - 608q^{58} - 2884q^{64} + 422q^{70} - 8q^{73} - 2916q^{76} + 4q^{79} - 1440q^{82} + 4198q^{88} - 5472q^{94} + 4q^{97} + O(q^{100}) \)

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

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