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Properties

Label 432.4.bj
Level $432$
Weight $4$
Character orbit 432.bj
Rep. character $\chi_{432}(11,\cdot)$
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.bj (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

\( 2568 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 18 q^{8} + O(q^{10}) \) \( 2568 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 18 q^{8} - 6 q^{10} - 12 q^{11} + 222 q^{12} - 12 q^{13} - 12 q^{14} - 12 q^{16} - 36 q^{17} - 12 q^{18} - 6 q^{19} - 474 q^{20} - 12 q^{21} - 12 q^{22} - 24 q^{23} - 762 q^{24} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{32} - 24 q^{33} - 60 q^{34} - 18 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 24 q^{39} - 12 q^{40} + 4728 q^{42} - 12 q^{43} - 18 q^{44} - 12 q^{45} - 6 q^{46} - 12 q^{48} - 24 q^{49} - 6408 q^{50} - 174 q^{51} - 12 q^{52} + 8892 q^{54} - 48 q^{55} - 2070 q^{56} + 1770 q^{58} + 3048 q^{59} - 3672 q^{60} - 12 q^{61} - 3780 q^{62} - 6 q^{64} - 24 q^{65} + 13566 q^{66} - 12 q^{67} + 4206 q^{68} - 12 q^{69} + 2046 q^{70} - 36 q^{71} + 9024 q^{72} + 5448 q^{74} - 4968 q^{75} - 12 q^{76} - 12 q^{77} + 2250 q^{78} - 24 q^{81} - 24 q^{82} - 3672 q^{83} + 1104 q^{84} - 762 q^{85} - 8352 q^{86} - 24 q^{87} - 12 q^{88} - 4386 q^{90} - 6 q^{91} + 9450 q^{92} - 12 q^{93} - 12 q^{94} - 5088 q^{96} - 24 q^{97} - 18 q^{98} - 12 q^{99} + O(q^{100}) \)

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.