Properties

Label 108.3.j
Level 108
Weight 3
Character orbit j
Rep. character \(\chi_{108}(7,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 204
Newform subspaces 1
Sturm bound 54
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.j (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).

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

Trace form

\( 204q - 6q^{2} - 6q^{4} - 12q^{5} - 6q^{6} - 3q^{8} - 12q^{9} + O(q^{10}) \) \( 204q - 6q^{2} - 6q^{4} - 12q^{5} - 6q^{6} - 3q^{8} - 12q^{9} - 3q^{10} + 39q^{12} - 12q^{13} + 39q^{14} - 6q^{16} - 6q^{17} - 27q^{18} - 69q^{20} - 12q^{21} - 6q^{22} - 138q^{24} - 12q^{25} - 174q^{26} - 12q^{28} + 60q^{29} - 153q^{30} - 96q^{32} + 48q^{33} + 6q^{34} + 24q^{36} - 6q^{37} + 72q^{38} + 69q^{40} - 192q^{41} - 126q^{42} - 219q^{44} - 132q^{45} - 3q^{46} - 219q^{48} - 12q^{49} - 165q^{50} + 21q^{52} - 24q^{53} + 78q^{54} + 99q^{56} - 150q^{57} - 141q^{58} + 210q^{60} - 12q^{61} + 294q^{62} - 3q^{64} - 156q^{65} + 393q^{66} + 375q^{68} - 60q^{69} - 165q^{70} + 228q^{72} - 6q^{73} + 447q^{74} - 54q^{76} + 132q^{77} + 750q^{78} + 798q^{80} + 228q^{81} - 12q^{82} + 762q^{84} + 138q^{85} + 606q^{86} - 198q^{88} - 114q^{89} + 894q^{90} + 723q^{92} - 1020q^{93} - 357q^{94} + 474q^{96} + 168q^{97} + 510q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.3.j.a \(204\) \(2.943\) None \(-6\) \(0\) \(-12\) \(0\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database