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Properties

Label 648.3.z
Level $648$
Weight $3$
Character orbit 648.z
Rep. character $\chi_{648}(5,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $3852$
Sturm bound $324$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 648.z (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 648 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(324\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(648, [\chi])\).

Total New Old
Modular forms 3924 3924 0
Cusp forms 3852 3852 0
Eisenstein series 72 72 0

Trace form

\( 3852 q - 18 q^{2} - 18 q^{4} - 18 q^{6} - 36 q^{7} - 18 q^{8} - 36 q^{9} + O(q^{10}) \) \( 3852 q - 18 q^{2} - 18 q^{4} - 18 q^{6} - 36 q^{7} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 18 q^{14} - 36 q^{15} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 18 q^{22} - 36 q^{23} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 18 q^{30} - 36 q^{31} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 18 q^{38} - 36 q^{39} - 18 q^{40} - 36 q^{41} - 513 q^{42} + 630 q^{44} - 18 q^{46} - 36 q^{47} + 477 q^{48} - 36 q^{49} - 369 q^{50} - 18 q^{52} + 108 q^{54} - 18 q^{55} - 396 q^{56} - 36 q^{57} - 18 q^{58} - 837 q^{60} + 873 q^{62} - 36 q^{63} - 18 q^{64} - 36 q^{65} + 918 q^{66} - 693 q^{68} - 18 q^{70} - 36 q^{71} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} + 63 q^{78} - 36 q^{79} - 36 q^{81} - 36 q^{82} - 99 q^{84} - 18 q^{86} - 36 q^{87} - 18 q^{88} - 36 q^{89} + 1053 q^{90} + 1332 q^{92} - 18 q^{94} - 36 q^{95} + 1269 q^{96} - 36 q^{97} + 1521 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(648, [\chi])\) into newform subspaces

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