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Properties

Label 432.6.bg
Level $432$
Weight $6$
Character orbit 432.bg
Rep. character $\chi_{432}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $4296$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.bg (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(432, [\chi])\).

Total New Old
Modular forms 4344 4344 0
Cusp forms 4296 4296 0
Eisenstein series 48 48 0

Trace form

\( 4296 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} + O(q^{10}) \) \( 4296 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 6 q^{10} - 12 q^{11} + 2346 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 12 q^{18} - 6 q^{19} + 2466 q^{20} - 12 q^{21} - 12 q^{22} - 16542 q^{24} - 24 q^{26} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 24 q^{33} + 180 q^{34} - 6 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 12 q^{40} - 69552 q^{42} - 12 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 24 q^{47} - 12 q^{48} - 24 q^{49} - 192048 q^{50} + 1446 q^{51} - 12 q^{52} - 24 q^{53} + 462828 q^{54} - 100854 q^{56} - 19506 q^{58} + 45744 q^{59} + 212328 q^{60} - 12 q^{61} - 307632 q^{62} - 24 q^{63} - 6 q^{64} - 24 q^{65} + 49518 q^{66} - 12 q^{67} - 217650 q^{68} - 12 q^{69} - 100854 q^{70} - 614016 q^{72} - 298968 q^{74} - 191616 q^{75} - 12 q^{76} - 12 q^{77} + 232506 q^{78} - 24 q^{79} + 1166196 q^{80} - 24 q^{81} - 24 q^{82} - 493872 q^{83} + 617508 q^{84} + 18738 q^{85} + 1728 q^{86} - 12 q^{88} - 354306 q^{90} - 6 q^{91} + 690942 q^{92} - 12 q^{93} - 12 q^{94} - 24 q^{95} + 269448 q^{96} - 24 q^{97} - 6 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

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