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Properties

Label 648.4.t
Level $648$
Weight $4$
Character orbit 648.t
Rep. character $\chi_{648}(37,\cdot)$
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.t (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

\( 636 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} + O(q^{10}) \) \( 636 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} - 69 q^{14} - 6 q^{16} + 6 q^{17} + 237 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 1002 q^{26} - 12 q^{28} - 12 q^{31} - 684 q^{32} + 18 q^{34} - 840 q^{38} - 381 q^{40} - 48 q^{41} - 885 q^{44} - 3 q^{46} + 12 q^{47} - 12 q^{49} - 2817 q^{50} + 1371 q^{52} - 24 q^{55} + 2925 q^{56} - 897 q^{58} + 630 q^{62} - 3 q^{64} + 12 q^{65} - 2595 q^{68} + 999 q^{70} - 5958 q^{71} - 6 q^{73} + 5931 q^{74} - 198 q^{76} - 12 q^{79} - 78 q^{80} - 12 q^{82} - 8322 q^{86} - 1542 q^{88} + 6 q^{89} - 3243 q^{92} - 2031 q^{94} + 762 q^{95} - 12 q^{97} + 972 q^{98} + O(q^{100}) \)

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

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