Properties

Label 18.3.d
Level 18
Weight 3
Character orbit d
Rep. character \(\chi_{18}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 18.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(18, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\(4q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 36q^{14} \) \(\mathstrut +\mathstrut 18q^{15} \) \(\mathstrut -\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 36q^{20} \) \(\mathstrut -\mathstrut 42q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 18q^{23} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 72q^{30} \) \(\mathstrut +\mathstrut 38q^{31} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 128q^{37} \) \(\mathstrut -\mathstrut 72q^{38} \) \(\mathstrut -\mathstrut 102q^{39} \) \(\mathstrut -\mathstrut 126q^{41} \) \(\mathstrut -\mathstrut 48q^{42} \) \(\mathstrut -\mathstrut 46q^{43} \) \(\mathstrut -\mathstrut 54q^{45} \) \(\mathstrut -\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 54q^{47} \) \(\mathstrut +\mathstrut 24q^{48} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 72q^{51} \) \(\mathstrut +\mathstrut 20q^{52} \) \(\mathstrut +\mathstrut 36q^{54} \) \(\mathstrut -\mathstrut 108q^{55} \) \(\mathstrut +\mathstrut 72q^{56} \) \(\mathstrut +\mathstrut 144q^{57} \) \(\mathstrut +\mathstrut 24q^{58} \) \(\mathstrut +\mathstrut 126q^{59} \) \(\mathstrut -\mathstrut 36q^{60} \) \(\mathstrut +\mathstrut 62q^{61} \) \(\mathstrut +\mathstrut 222q^{63} \) \(\mathstrut -\mathstrut 32q^{64} \) \(\mathstrut +\mathstrut 90q^{65} \) \(\mathstrut -\mathstrut 72q^{66} \) \(\mathstrut -\mathstrut 106q^{67} \) \(\mathstrut +\mathstrut 72q^{68} \) \(\mathstrut +\mathstrut 18q^{69} \) \(\mathstrut -\mathstrut 108q^{70} \) \(\mathstrut -\mathstrut 96q^{72} \) \(\mathstrut -\mathstrut 208q^{73} \) \(\mathstrut +\mathstrut 72q^{74} \) \(\mathstrut -\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 90q^{77} \) \(\mathstrut +\mathstrut 144q^{78} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 252q^{81} \) \(\mathstrut +\mathstrut 144q^{82} \) \(\mathstrut -\mathstrut 378q^{83} \) \(\mathstrut -\mathstrut 144q^{84} \) \(\mathstrut +\mathstrut 108q^{85} \) \(\mathstrut -\mathstrut 108q^{86} \) \(\mathstrut -\mathstrut 54q^{87} \) \(\mathstrut +\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 412q^{91} \) \(\mathstrut +\mathstrut 36q^{92} \) \(\mathstrut +\mathstrut 222q^{93} \) \(\mathstrut +\mathstrut 84q^{94} \) \(\mathstrut +\mathstrut 180q^{95} \) \(\mathstrut +\mathstrut 48q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut 126q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(18, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
18.3.d.a \(4\) \(0.490\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-18\) \(2\) \(q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)