Properties

Label 648.4.bd
Level $648$
Weight $4$
Character orbit 648.bd
Rep. character $\chi_{648}(13,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $5796$
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.bd (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 648 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 5868 5868 0
Cusp forms 5796 5796 0
Eisenstein series 72 72 0

Trace form

\( 5796q - 18q^{2} - 18q^{4} - 18q^{6} - 36q^{7} - 18q^{8} - 36q^{9} + O(q^{10}) \) \( 5796q - 18q^{2} - 18q^{4} - 18q^{6} - 36q^{7} - 18q^{8} - 36q^{9} - 18q^{10} - 18q^{12} - 18q^{14} - 36q^{15} - 18q^{16} - 36q^{17} - 18q^{18} - 18q^{20} - 18q^{22} - 36q^{23} - 18q^{24} - 36q^{25} - 9q^{26} - 9q^{28} - 18q^{30} - 36q^{31} - 18q^{32} - 36q^{33} - 18q^{34} - 18q^{36} - 18q^{38} - 36q^{39} - 18q^{40} - 36q^{41} + 3537q^{42} - 2682q^{44} - 18q^{46} - 36q^{47} + 2259q^{48} - 36q^{49} - 4815q^{50} - 18q^{52} - 6696q^{54} - 18q^{55} + 5904q^{56} - 36q^{57} - 18q^{58} + 1269q^{60} + 1863q^{62} - 36q^{63} - 18q^{64} - 36q^{65} + 7398q^{66} - 7083q^{68} - 18q^{70} - 36q^{71} - 18q^{72} - 36q^{73} - 18q^{74} - 18q^{76} - 261q^{78} - 36q^{79} - 36q^{80} - 36q^{81} - 36q^{82} - 261q^{84} - 18q^{86} - 36q^{87} - 18q^{88} - 36q^{89} - 12555q^{90} - 11988q^{92} - 18q^{94} - 36q^{95} - 2943q^{96} - 36q^{97} + 2889q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(648, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.