Properties

Label 18.5.d
Level 18
Weight 5
Character orbit d
Rep. character \(\chi_{18}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 8
Newforms 1
Sturm bound 15
Trace bound 0

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 5 \)
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: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(18, [\chi])\).

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\(8q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 48q^{6} \) \(\mathstrut -\mathstrut 26q^{7} \) \(\mathstrut -\mathstrut 78q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 48q^{6} \) \(\mathstrut -\mathstrut 26q^{7} \) \(\mathstrut -\mathstrut 78q^{9} \) \(\mathstrut -\mathstrut 720q^{11} \) \(\mathstrut -\mathstrut 144q^{12} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 288q^{14} \) \(\mathstrut +\mathstrut 1134q^{15} \) \(\mathstrut -\mathstrut 256q^{16} \) \(\mathstrut -\mathstrut 384q^{18} \) \(\mathstrut +\mathstrut 100q^{19} \) \(\mathstrut +\mathstrut 144q^{20} \) \(\mathstrut +\mathstrut 438q^{21} \) \(\mathstrut +\mathstrut 336q^{22} \) \(\mathstrut +\mathstrut 1278q^{23} \) \(\mathstrut +\mathstrut 384q^{24} \) \(\mathstrut +\mathstrut 794q^{25} \) \(\mathstrut -\mathstrut 1296q^{27} \) \(\mathstrut -\mathstrut 416q^{28} \) \(\mathstrut -\mathstrut 1854q^{29} \) \(\mathstrut -\mathstrut 3456q^{30} \) \(\mathstrut -\mathstrut 1478q^{31} \) \(\mathstrut -\mathstrut 3384q^{33} \) \(\mathstrut -\mathstrut 96q^{34} \) \(\mathstrut +\mathstrut 1056q^{36} \) \(\mathstrut -\mathstrut 32q^{37} \) \(\mathstrut +\mathstrut 6768q^{38} \) \(\mathstrut +\mathstrut 5274q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut +\mathstrut 2592q^{42} \) \(\mathstrut -\mathstrut 68q^{43} \) \(\mathstrut +\mathstrut 3402q^{45} \) \(\mathstrut +\mathstrut 2112q^{46} \) \(\mathstrut +\mathstrut 2214q^{47} \) \(\mathstrut -\mathstrut 1536q^{48} \) \(\mathstrut +\mathstrut 2442q^{49} \) \(\mathstrut -\mathstrut 15552q^{50} \) \(\mathstrut -\mathstrut 12006q^{51} \) \(\mathstrut -\mathstrut 80q^{52} \) \(\mathstrut +\mathstrut 7056q^{54} \) \(\mathstrut -\mathstrut 3996q^{55} \) \(\mathstrut +\mathstrut 2304q^{56} \) \(\mathstrut +\mathstrut 10902q^{57} \) \(\mathstrut -\mathstrut 2400q^{58} \) \(\mathstrut +\mathstrut 9108q^{59} \) \(\mathstrut +\mathstrut 6480q^{60} \) \(\mathstrut -\mathstrut 4478q^{61} \) \(\mathstrut -\mathstrut 6654q^{63} \) \(\mathstrut -\mathstrut 4096q^{64} \) \(\mathstrut -\mathstrut 22554q^{65} \) \(\mathstrut -\mathstrut 19872q^{66} \) \(\mathstrut +\mathstrut 7504q^{67} \) \(\mathstrut -\mathstrut 11088q^{68} \) \(\mathstrut -\mathstrut 5994q^{69} \) \(\mathstrut +\mathstrut 6048q^{70} \) \(\mathstrut +\mathstrut 5376q^{72} \) \(\mathstrut +\mathstrut 20716q^{73} \) \(\mathstrut +\mathstrut 15264q^{74} \) \(\mathstrut +\mathstrut 16590q^{75} \) \(\mathstrut +\mathstrut 400q^{76} \) \(\mathstrut +\mathstrut 34434q^{77} \) \(\mathstrut +\mathstrut 24096q^{78} \) \(\mathstrut -\mathstrut 6050q^{79} \) \(\mathstrut -\mathstrut 21150q^{81} \) \(\mathstrut +\mathstrut 1152q^{82} \) \(\mathstrut -\mathstrut 3834q^{83} \) \(\mathstrut -\mathstrut 9600q^{84} \) \(\mathstrut -\mathstrut 16092q^{85} \) \(\mathstrut -\mathstrut 12528q^{86} \) \(\mathstrut +\mathstrut 10170q^{87} \) \(\mathstrut -\mathstrut 2688q^{88} \) \(\mathstrut +\mathstrut 2592q^{90} \) \(\mathstrut -\mathstrut 45868q^{91} \) \(\mathstrut +\mathstrut 10224q^{92} \) \(\mathstrut -\mathstrut 10926q^{93} \) \(\mathstrut +\mathstrut 672q^{94} \) \(\mathstrut +\mathstrut 20880q^{95} \) \(\mathstrut +\mathstrut 31336q^{97} \) \(\mathstrut -\mathstrut 22338q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(18, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
18.5.d.a \(8\) \(1.861\) 8.0.\(\cdots\).4 None \(0\) \(6\) \(18\) \(-26\) \(q-\beta _{3}q^{2}+(2+\beta _{1}-3\beta _{2}-\beta _{5})q^{3}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)