Properties

Label 18.2.c
Level 18
Weight 2
Character orbit c
Rep. character \(\chi_{18}(7,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(18, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 3q^{34} \) \(\mathstrut +\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut -\mathstrut 2q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 8q^{62} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 3q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut +\mathstrut q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut +\mathstrut q^{86} \) \(\mathstrut +\mathstrut 18q^{87} \) \(\mathstrut +\mathstrut 3q^{88} \) \(\mathstrut +\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 6q^{94} \) \(\mathstrut -\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut 18q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(18, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
18.2.c.a \(2\) \(0.144\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(-2\) \(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)