Properties

Label 5.18.b
Level 5
Weight 18
Character orbit b
Rep. character \(\chi_{5}(4,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

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

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

Trace form

\(8q \) \(\mathstrut -\mathstrut 579096q^{4} \) \(\mathstrut +\mathstrut 379200q^{5} \) \(\mathstrut +\mathstrut 357816q^{6} \) \(\mathstrut -\mathstrut 234916344q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 579096q^{4} \) \(\mathstrut +\mathstrut 379200q^{5} \) \(\mathstrut +\mathstrut 357816q^{6} \) \(\mathstrut -\mathstrut 234916344q^{9} \) \(\mathstrut +\mathstrut 329570200q^{10} \) \(\mathstrut +\mathstrut 463296576q^{11} \) \(\mathstrut -\mathstrut 29937907992q^{14} \) \(\mathstrut +\mathstrut 30646226400q^{15} \) \(\mathstrut +\mathstrut 30848001568q^{16} \) \(\mathstrut -\mathstrut 20615713280q^{19} \) \(\mathstrut -\mathstrut 47558579400q^{20} \) \(\mathstrut -\mathstrut 75039699024q^{21} \) \(\mathstrut +\mathstrut 1768741136160q^{24} \) \(\mathstrut -\mathstrut 1789249435000q^{25} \) \(\mathstrut -\mathstrut 838901194224q^{26} \) \(\mathstrut -\mathstrut 4079017824720q^{29} \) \(\mathstrut +\mathstrut 2416984007400q^{30} \) \(\mathstrut +\mathstrut 11329328658496q^{31} \) \(\mathstrut -\mathstrut 36406243632832q^{34} \) \(\mathstrut +\mathstrut 4019663899200q^{35} \) \(\mathstrut +\mathstrut 59729752432728q^{36} \) \(\mathstrut +\mathstrut 40318460422272q^{39} \) \(\mathstrut -\mathstrut 209747532172000q^{40} \) \(\mathstrut +\mathstrut 97217252847456q^{41} \) \(\mathstrut -\mathstrut 116357853210912q^{44} \) \(\mathstrut -\mathstrut 366841998003600q^{45} \) \(\mathstrut +\mathstrut 1081224261700136q^{46} \) \(\mathstrut -\mathstrut 856574357621656q^{49} \) \(\mathstrut -\mathstrut 1283266301910000q^{50} \) \(\mathstrut +\mathstrut 2468309514424896q^{51} \) \(\mathstrut -\mathstrut 3408409774777680q^{54} \) \(\mathstrut -\mathstrut 2042713226757600q^{55} \) \(\mathstrut +\mathstrut 8363016326678880q^{56} \) \(\mathstrut -\mathstrut 1091409512240640q^{59} \) \(\mathstrut -\mathstrut 11479379108104800q^{60} \) \(\mathstrut +\mathstrut 8064731010774976q^{61} \) \(\mathstrut -\mathstrut 3616160324265856q^{64} \) \(\mathstrut -\mathstrut 11989509557901600q^{65} \) \(\mathstrut +\mathstrut 27318846906958752q^{66} \) \(\mathstrut -\mathstrut 12078989597365008q^{69} \) \(\mathstrut -\mathstrut 13190931213697800q^{70} \) \(\mathstrut +\mathstrut 25241492058140736q^{71} \) \(\mathstrut -\mathstrut 29902523510328912q^{74} \) \(\mathstrut +\mathstrut 3839235716880000q^{75} \) \(\mathstrut +\mathstrut 20767634734678560q^{76} \) \(\mathstrut +\mathstrut 3229852337730880q^{79} \) \(\mathstrut +\mathstrut 1263407265391200q^{80} \) \(\mathstrut -\mathstrut 49353541005202632q^{81} \) \(\mathstrut +\mathstrut 101439947332382688q^{84} \) \(\mathstrut +\mathstrut 25693702369787200q^{85} \) \(\mathstrut -\mathstrut 165112838769552744q^{86} \) \(\mathstrut +\mathstrut 92963987535626640q^{89} \) \(\mathstrut +\mathstrut 206315814421823400q^{90} \) \(\mathstrut -\mathstrut 225591670236809664q^{91} \) \(\mathstrut +\mathstrut 162612564681867848q^{94} \) \(\mathstrut +\mathstrut 204319715505252000q^{95} \) \(\mathstrut -\mathstrut 654303222993538944q^{96} \) \(\mathstrut -\mathstrut 56327331239952768q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.18.b.a \(8\) \(9.161\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(379200\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-72387+\beta _{3}+\cdots)q^{4}+\cdots\)