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Properties

Label 432.4.bg
Level $432$
Weight $4$
Character orbit 432.bg
Rep. character $\chi_{432}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2568$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 432.bg (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(432, [\chi])\).

Total New Old
Modular forms 2616 2616 0
Cusp forms 2568 2568 0
Eisenstein series 48 48 0

Trace form

\( 2568 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} + O(q^{10}) \) \( 2568 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 246 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 12 q^{18} - 6 q^{19} + 450 q^{20} - 12 q^{21} - 12 q^{22} + 738 q^{24} - 24 q^{26} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 24 q^{33} + 36 q^{34} - 6 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 12 q^{40} - 4752 q^{42} - 12 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 24 q^{47} - 12 q^{48} - 24 q^{49} + 6384 q^{50} + 150 q^{51} - 12 q^{52} - 24 q^{53} - 8916 q^{54} - 2070 q^{56} - 1794 q^{58} - 3072 q^{59} - 3672 q^{60} - 12 q^{61} + 1248 q^{62} - 24 q^{63} - 6 q^{64} - 24 q^{65} - 6210 q^{66} - 12 q^{67} + 4974 q^{68} - 12 q^{69} - 2070 q^{70} + 2880 q^{72} + 5448 q^{74} + 4944 q^{75} - 12 q^{76} - 12 q^{77} + 2250 q^{78} - 24 q^{79} - 204 q^{80} - 24 q^{81} - 24 q^{82} + 3648 q^{83} - 12348 q^{84} + 738 q^{85} - 8352 q^{86} - 12 q^{88} - 4386 q^{90} - 6 q^{91} - 9474 q^{92} - 12 q^{93} - 12 q^{94} - 24 q^{95} + 5064 q^{96} - 24 q^{97} - 6 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

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