Properties

Label 432.2.bj
Level 432
Weight 2
Character orbit bj
Rep. character \(\chi_{432}(11,\cdot)\)
Character field \(\Q(\zeta_{36})\)
Dimension 840
Newform subspaces 1
Sturm bound 144
Trace bound 0

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 432.bj (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).

Total New Old
Modular forms 888 888 0
Cusp forms 840 840 0
Eisenstein series 48 48 0

Trace form

\( 840q - 12q^{2} - 12q^{3} - 12q^{4} - 12q^{5} - 12q^{6} - 24q^{7} - 18q^{8} + O(q^{10}) \) \( 840q - 12q^{2} - 12q^{3} - 12q^{4} - 12q^{5} - 12q^{6} - 24q^{7} - 18q^{8} - 6q^{10} - 12q^{11} + 6q^{12} - 12q^{13} - 12q^{14} - 12q^{16} - 36q^{17} - 12q^{18} - 6q^{19} + 30q^{20} - 12q^{21} - 12q^{22} - 24q^{23} - 42q^{24} - 12q^{27} - 24q^{28} - 12q^{29} - 12q^{30} - 12q^{32} - 24q^{33} - 24q^{34} - 18q^{35} - 12q^{36} - 6q^{37} - 12q^{38} - 24q^{39} - 12q^{40} + 48q^{42} - 12q^{43} - 18q^{44} - 12q^{45} - 6q^{46} - 12q^{48} - 24q^{49} + 144q^{50} - 30q^{51} - 12q^{52} - 180q^{54} - 48q^{55} - 54q^{56} - 66q^{58} + 24q^{59} - 72q^{60} - 12q^{61} - 216q^{62} - 6q^{64} - 24q^{65} - 6q^{66} - 12q^{67} - 114q^{68} - 12q^{69} + 30q^{70} - 36q^{71} - 48q^{72} - 96q^{74} + 72q^{75} - 12q^{76} - 12q^{77} - 90q^{78} - 24q^{81} - 24q^{82} - 72q^{83} - 192q^{84} - 42q^{85} - 72q^{86} - 24q^{87} - 12q^{88} - 66q^{90} - 6q^{91} - 126q^{92} - 12q^{93} - 12q^{94} + 96q^{96} - 24q^{97} - 18q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
432.2.bj.a \(840\) \(3.450\) None \(-12\) \(-12\) \(-12\) \(-24\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database