Properties

Label 216.2.t
Level 216
Weight 2
Character orbit t
Rep. character \(\chi_{216}(13,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 204
Newform subspaces 1
Sturm bound 72
Trace bound 0

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Defining parameters

Level: \( N \) = \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 216.t (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(216, [\chi])\).

Total New Old
Modular forms 228 228 0
Cusp forms 204 204 0
Eisenstein series 24 24 0

Trace form

\( 204q - 6q^{2} - 6q^{4} - 6q^{6} - 12q^{7} - 3q^{8} - 12q^{9} + O(q^{10}) \) \( 204q - 6q^{2} - 6q^{4} - 6q^{6} - 12q^{7} - 3q^{8} - 12q^{9} - 3q^{10} + 3q^{12} - 21q^{14} - 12q^{15} - 6q^{16} - 6q^{17} - 27q^{18} + 15q^{20} - 6q^{22} - 12q^{23} - 12q^{25} - 30q^{26} - 12q^{28} - 39q^{30} - 12q^{31} - 36q^{32} - 36q^{36} - 42q^{38} - 12q^{39} - 21q^{40} - 24q^{41} - 66q^{42} + 21q^{44} - 3q^{46} - 12q^{47} + 51q^{48} - 12q^{49} - 99q^{50} - 33q^{52} - 90q^{54} - 24q^{55} + 99q^{56} - 30q^{57} + 21q^{58} + 102q^{60} - 36q^{62} - 72q^{63} - 3q^{64} - 12q^{65} - 9q^{66} + 75q^{68} + 9q^{70} - 90q^{71} + 60q^{72} - 6q^{73} + 9q^{74} - 18q^{76} + 12q^{78} - 12q^{79} + 78q^{80} - 12q^{81} - 12q^{82} + 102q^{84} - 30q^{86} - 48q^{87} - 30q^{88} - 6q^{89} + 6q^{90} + 111q^{92} - 33q^{94} - 42q^{95} + 126q^{96} - 12q^{97} + 54q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
216.2.t.a \(204\) \(1.725\) None \(-6\) \(0\) \(0\) \(-12\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database