Properties

Label 18.4.c
Level 18
Weight 4
Character orbit c
Rep. character \(\chi_{18}(7,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 6
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 18.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(18, [\chi])\).

Total New Old
Modular forms 22 6 16
Cusp forms 14 6 8
Eisenstein series 8 0 8

Trace form

\(6q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 105q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 105q^{9} \) \(\mathstrut +\mathstrut 39q^{11} \) \(\mathstrut +\mathstrut 24q^{12} \) \(\mathstrut -\mathstrut 24q^{13} \) \(\mathstrut +\mathstrut 100q^{14} \) \(\mathstrut +\mathstrut 90q^{15} \) \(\mathstrut -\mathstrut 48q^{16} \) \(\mathstrut -\mathstrut 78q^{17} \) \(\mathstrut +\mathstrut 156q^{18} \) \(\mathstrut +\mathstrut 210q^{19} \) \(\mathstrut +\mathstrut 72q^{20} \) \(\mathstrut -\mathstrut 36q^{21} \) \(\mathstrut -\mathstrut 18q^{22} \) \(\mathstrut -\mathstrut 264q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 219q^{25} \) \(\mathstrut -\mathstrut 392q^{26} \) \(\mathstrut -\mathstrut 96q^{28} \) \(\mathstrut -\mathstrut 348q^{29} \) \(\mathstrut -\mathstrut 288q^{30} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 32q^{32} \) \(\mathstrut +\mathstrut 765q^{33} \) \(\mathstrut +\mathstrut 90q^{34} \) \(\mathstrut +\mathstrut 1332q^{35} \) \(\mathstrut +\mathstrut 516q^{36} \) \(\mathstrut +\mathstrut 192q^{37} \) \(\mathstrut +\mathstrut 322q^{38} \) \(\mathstrut -\mathstrut 582q^{39} \) \(\mathstrut -\mathstrut 207q^{41} \) \(\mathstrut -\mathstrut 816q^{42} \) \(\mathstrut +\mathstrut 129q^{43} \) \(\mathstrut -\mathstrut 312q^{44} \) \(\mathstrut -\mathstrut 702q^{45} \) \(\mathstrut +\mathstrut 504q^{46} \) \(\mathstrut -\mathstrut 660q^{47} \) \(\mathstrut -\mathstrut 144q^{48} \) \(\mathstrut -\mathstrut 585q^{49} \) \(\mathstrut +\mathstrut 614q^{50} \) \(\mathstrut -\mathstrut 153q^{51} \) \(\mathstrut -\mathstrut 96q^{52} \) \(\mathstrut +\mathstrut 528q^{53} \) \(\mathstrut +\mathstrut 954q^{54} \) \(\mathstrut -\mathstrut 1404q^{55} \) \(\mathstrut +\mathstrut 400q^{56} \) \(\mathstrut +\mathstrut 987q^{57} \) \(\mathstrut +\mathstrut 252q^{58} \) \(\mathstrut -\mathstrut 327q^{59} \) \(\mathstrut -\mathstrut 936q^{60} \) \(\mathstrut +\mathstrut 858q^{61} \) \(\mathstrut -\mathstrut 1664q^{62} \) \(\mathstrut -\mathstrut 1794q^{63} \) \(\mathstrut +\mathstrut 384q^{64} \) \(\mathstrut +\mathstrut 414q^{65} \) \(\mathstrut +\mathstrut 288q^{66} \) \(\mathstrut +\mathstrut 1587q^{67} \) \(\mathstrut +\mathstrut 156q^{68} \) \(\mathstrut +\mathstrut 1494q^{69} \) \(\mathstrut +\mathstrut 216q^{70} \) \(\mathstrut -\mathstrut 312q^{71} \) \(\mathstrut -\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 258q^{73} \) \(\mathstrut +\mathstrut 856q^{74} \) \(\mathstrut +\mathstrut 3231q^{75} \) \(\mathstrut -\mathstrut 420q^{76} \) \(\mathstrut +\mathstrut 708q^{77} \) \(\mathstrut +\mathstrut 132q^{78} \) \(\mathstrut -\mathstrut 1482q^{79} \) \(\mathstrut -\mathstrut 576q^{80} \) \(\mathstrut +\mathstrut 315q^{81} \) \(\mathstrut -\mathstrut 2916q^{82} \) \(\mathstrut -\mathstrut 138q^{83} \) \(\mathstrut +\mathstrut 744q^{84} \) \(\mathstrut +\mathstrut 108q^{85} \) \(\mathstrut -\mathstrut 86q^{86} \) \(\mathstrut -\mathstrut 3204q^{87} \) \(\mathstrut -\mathstrut 72q^{88} \) \(\mathstrut -\mathstrut 3084q^{89} \) \(\mathstrut -\mathstrut 432q^{90} \) \(\mathstrut +\mathstrut 2508q^{91} \) \(\mathstrut -\mathstrut 1056q^{92} \) \(\mathstrut -\mathstrut 2634q^{93} \) \(\mathstrut +\mathstrut 612q^{94} \) \(\mathstrut -\mathstrut 2016q^{95} \) \(\mathstrut +\mathstrut 384q^{96} \) \(\mathstrut +\mathstrut 1029q^{97} \) \(\mathstrut +\mathstrut 2604q^{98} \) \(\mathstrut +\mathstrut 1152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(18, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
18.4.c.a \(2\) \(1.062\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(9\) \(31\) \(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b \(4\) \(1.062\) \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(4\) \(3\) \(9\) \(-19\) \(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)