Properties

Label 108.2.l
Level 108
Weight 2
Character orbit l
Rep. character \(\chi_{108}(11,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 96
Newform subspaces 1
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 108.l (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(108, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 96 96 0
Eisenstein series 24 24 0

Trace form

\( 96q - 6q^{2} - 6q^{4} - 12q^{5} - 6q^{6} - 9q^{8} - 12q^{9} + O(q^{10}) \) \( 96q - 6q^{2} - 6q^{4} - 12q^{5} - 6q^{6} - 9q^{8} - 12q^{9} - 3q^{10} - 15q^{12} - 12q^{13} - 21q^{14} - 6q^{16} - 18q^{17} - 27q^{18} - 27q^{20} - 12q^{21} - 6q^{22} - 12q^{24} - 12q^{25} - 12q^{28} - 24q^{29} + 9q^{30} + 24q^{32} - 42q^{33} - 12q^{34} + 24q^{36} - 6q^{37} + 18q^{38} - 21q^{40} - 42q^{41} + 54q^{42} + 63q^{44} - 24q^{45} - 3q^{46} + 69q^{48} - 12q^{49} + 87q^{50} - 33q^{52} + 78q^{54} + 99q^{56} - 24q^{57} - 33q^{58} + 102q^{60} - 12q^{61} + 90q^{62} - 3q^{64} + 12q^{65} + 87q^{66} + 51q^{68} + 12q^{69} - 21q^{70} + 12q^{72} - 6q^{73} + 21q^{74} - 18q^{76} + 12q^{77} - 24q^{78} + 12q^{81} - 12q^{82} - 12q^{84} - 42q^{85} - 30q^{86} + 18q^{88} - 78q^{90} - 123q^{92} + 60q^{93} + 21q^{94} - 138q^{96} - 30q^{97} - 180q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.2.l.a \(96\) \(0.862\) None \(-6\) \(0\) \(-12\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database