Properties

Label 5.20.b
Level 5
Weight 20
Character orbit b
Rep. character \(\chi_{5}(4,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 10
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(5, [\chi])\).

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

Trace form

\(8q \) \(\mathstrut -\mathstrut 1620744q^{4} \) \(\mathstrut +\mathstrut 147000q^{5} \) \(\mathstrut +\mathstrut 3365736q^{6} \) \(\mathstrut +\mathstrut 345358584q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 1620744q^{4} \) \(\mathstrut +\mathstrut 147000q^{5} \) \(\mathstrut +\mathstrut 3365736q^{6} \) \(\mathstrut +\mathstrut 345358584q^{9} \) \(\mathstrut -\mathstrut 610691000q^{10} \) \(\mathstrut -\mathstrut 3379575264q^{11} \) \(\mathstrut +\mathstrut 177250591032q^{14} \) \(\mathstrut -\mathstrut 242324628000q^{15} \) \(\mathstrut -\mathstrut 312730276832q^{16} \) \(\mathstrut +\mathstrut 4547188380640q^{19} \) \(\mathstrut -\mathstrut 4180429431000q^{20} \) \(\mathstrut -\mathstrut 2983154334624q^{21} \) \(\mathstrut -\mathstrut 6176642779680q^{24} \) \(\mathstrut +\mathstrut 17715709625000q^{25} \) \(\mathstrut +\mathstrut 15909228128496q^{26} \) \(\mathstrut -\mathstrut 188222300345040q^{29} \) \(\mathstrut +\mathstrut 148501482939000q^{30} \) \(\mathstrut +\mathstrut 72115006686976q^{31} \) \(\mathstrut +\mathstrut 378440221985792q^{34} \) \(\mathstrut -\mathstrut 299115755916000q^{35} \) \(\mathstrut -\mathstrut 964020253238712q^{36} \) \(\mathstrut +\mathstrut 3011653788049728q^{39} \) \(\mathstrut -\mathstrut 213611427940000q^{40} \) \(\mathstrut -\mathstrut 3314269428857904q^{41} \) \(\mathstrut +\mathstrut 489119304867552q^{44} \) \(\mathstrut +\mathstrut 10198157211261000q^{45} \) \(\mathstrut -\mathstrut 13716870314831944q^{46} \) \(\mathstrut -\mathstrut 11129258011816744q^{49} \) \(\mathstrut +\mathstrut 50375043666750000q^{50} \) \(\mathstrut -\mathstrut 46867071411404544q^{51} \) \(\mathstrut +\mathstrut 86068650834185040q^{54} \) \(\mathstrut +\mathstrut 69821226326124000q^{55} \) \(\mathstrut -\mathstrut 303831778832907360q^{56} \) \(\mathstrut +\mathstrut 259648032778012320q^{59} \) \(\mathstrut +\mathstrut 318110620655844000q^{60} \) \(\mathstrut -\mathstrut 582893562753226064q^{61} \) \(\mathstrut +\mathstrut 525415747276109696q^{64} \) \(\mathstrut +\mathstrut 747545324689032000q^{65} \) \(\mathstrut -\mathstrut 1871067587999976288q^{66} \) \(\mathstrut +\mathstrut 302144302523815008q^{69} \) \(\mathstrut +\mathstrut 2638361065839633000q^{70} \) \(\mathstrut -\mathstrut 2617007600602926144q^{71} \) \(\mathstrut +\mathstrut 1847591013622215312q^{74} \) \(\mathstrut +\mathstrut 2877932428209000000q^{75} \) \(\mathstrut -\mathstrut 7494494299858276320q^{76} \) \(\mathstrut +\mathstrut 3935092091109861760q^{79} \) \(\mathstrut +\mathstrut 5465139505859292000q^{80} \) \(\mathstrut -\mathstrut 8328177293660704152q^{81} \) \(\mathstrut +\mathstrut 7683875738824129632q^{84} \) \(\mathstrut +\mathstrut 3752387009219584000q^{85} \) \(\mathstrut -\mathstrut 14358563079146095224q^{86} \) \(\mathstrut +\mathstrut 2120141101636921680q^{89} \) \(\mathstrut +\mathstrut 7589596726146267000q^{90} \) \(\mathstrut -\mathstrut 3358638219973817664q^{91} \) \(\mathstrut -\mathstrut 10251771654977709928q^{94} \) \(\mathstrut +\mathstrut 6106065789884820000q^{95} \) \(\mathstrut +\mathstrut 15670161523483353216q^{96} \) \(\mathstrut -\mathstrut 16256944625235082272q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.20.b.a \(8\) \(11.441\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(147000\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-202593+\cdots)q^{4}+\cdots\)