Properties

Label 5.8.b
Level 5
Weight 8
Character orbit b
Rep. character \(\chi_{5}(4,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(5, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\(2q \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 150q^{5} \) \(\mathstrut -\mathstrut 696q^{6} \) \(\mathstrut +\mathstrut 2286q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 150q^{5} \) \(\mathstrut -\mathstrut 696q^{6} \) \(\mathstrut +\mathstrut 2286q^{9} \) \(\mathstrut +\mathstrut 5800q^{10} \) \(\mathstrut -\mathstrut 13656q^{11} \) \(\mathstrut +\mathstrut 9048q^{14} \) \(\mathstrut +\mathstrut 17400q^{15} \) \(\mathstrut -\mathstrut 29408q^{16} \) \(\mathstrut +\mathstrut 13720q^{19} \) \(\mathstrut +\mathstrut 1800q^{20} \) \(\mathstrut +\mathstrut 27144q^{21} \) \(\mathstrut -\mathstrut 97440q^{24} \) \(\mathstrut -\mathstrut 133750q^{25} \) \(\mathstrut +\mathstrut 218544q^{26} \) \(\mathstrut +\mathstrut 51180q^{29} \) \(\mathstrut -\mathstrut 52200q^{30} \) \(\mathstrut +\mathstrut 164224q^{31} \) \(\mathstrut -\mathstrut 337792q^{34} \) \(\mathstrut -\mathstrut 226200q^{35} \) \(\mathstrut +\mathstrut 27432q^{36} \) \(\mathstrut +\mathstrut 655632q^{39} \) \(\mathstrut +\mathstrut 812000q^{40} \) \(\mathstrut -\mathstrut 1066236q^{41} \) \(\mathstrut -\mathstrut 163872q^{44} \) \(\mathstrut +\mathstrut 171450q^{45} \) \(\mathstrut -\mathstrut 629416q^{46} \) \(\mathstrut +\mathstrut 1294214q^{49} \) \(\mathstrut +\mathstrut 870000q^{50} \) \(\mathstrut -\mathstrut 1013376q^{51} \) \(\mathstrut -\mathstrut 2317680q^{54} \) \(\mathstrut -\mathstrut 1024200q^{55} \) \(\mathstrut +\mathstrut 1266720q^{56} \) \(\mathstrut +\mathstrut 2877960q^{59} \) \(\mathstrut +\mathstrut 208800q^{60} \) \(\mathstrut +\mathstrut 2762044q^{61} \) \(\mathstrut -\mathstrut 4510336q^{64} \) \(\mathstrut -\mathstrut 5463600q^{65} \) \(\mathstrut +\mathstrut 4752288q^{66} \) \(\mathstrut -\mathstrut 1888248q^{69} \) \(\mathstrut +\mathstrut 678600q^{70} \) \(\mathstrut -\mathstrut 963216q^{71} \) \(\mathstrut +\mathstrut 4814928q^{74} \) \(\mathstrut +\mathstrut 2610000q^{75} \) \(\mathstrut +\mathstrut 164640q^{76} \) \(\mathstrut -\mathstrut 2119520q^{79} \) \(\mathstrut -\mathstrut 2205600q^{80} \) \(\mathstrut -\mathstrut 1953558q^{81} \) \(\mathstrut +\mathstrut 325728q^{84} \) \(\mathstrut +\mathstrut 8444800q^{85} \) \(\mathstrut -\mathstrut 15270936q^{86} \) \(\mathstrut +\mathstrut 11288340q^{89} \) \(\mathstrut +\mathstrut 6629400q^{90} \) \(\mathstrut -\mathstrut 8523216q^{91} \) \(\mathstrut -\mathstrut 125512q^{94} \) \(\mathstrut +\mathstrut 1029000q^{95} \) \(\mathstrut -\mathstrut 2238336q^{96} \) \(\mathstrut -\mathstrut 15608808q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.8.b.a \(2\) \(1.562\) \(\Q(\sqrt{-29}) \) None \(0\) \(0\) \(150\) \(0\) \(q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots\)