# Properties

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

# Related objects

## 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: $$\Q$$ Newform subspaces: $$1$$ 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

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

## Decomposition of $$S_{8}^{\mathrm{new}}(5, [\chi])$$ into newform subspaces

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 $$0$$ $$0$$ $$150$$ $$0$$ $$q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 - 140 T^{2} + 16384 T^{4}$$
$3$ $$1 - 3330 T^{2} + 4782969 T^{4}$$
$5$ $$1 - 150 T + 78125 T^{2}$$
$7$ $$1 - 1470650 T^{2} + 678223072849 T^{4}$$
$11$ $$( 1 + 6828 T + 19487171 T^{2} )^{2}$$
$13$ $$1 - 22562810 T^{2} + 3937376385699289 T^{4}$$
$17$ $$1 - 574764770 T^{2} + 168377826559400929 T^{4}$$
$19$ $$( 1 - 6860 T + 893871739 T^{2} )^{2}$$
$23$ $$1 - 5955848090 T^{2} + 11592836324538749809 T^{4}$$
$29$ $$( 1 - 25590 T + 17249876309 T^{2} )^{2}$$
$31$ $$( 1 - 82112 T + 27512614111 T^{2} )^{2}$$
$37$ $$1 - 139899246410 T^{2} +$$$$90\!\cdots\!89$$$$T^{4}$$
$41$ $$( 1 + 533118 T + 194754273881 T^{2} )^{2}$$
$43$ $$1 - 41047812050 T^{2} +$$$$73\!\cdots\!49$$$$T^{4}$$
$47$ $$1 - 1013212289930 T^{2} +$$$$25\!\cdots\!69$$$$T^{4}$$
$53$ $$1 - 2002060594730 T^{2} +$$$$13\!\cdots\!69$$$$T^{4}$$
$59$ $$( 1 - 1438980 T + 2488651484819 T^{2} )^{2}$$
$61$ $$( 1 - 1381022 T + 3142742836021 T^{2} )^{2}$$
$67$ $$1 - 4750924642370 T^{2} +$$$$36\!\cdots\!29$$$$T^{4}$$
$71$ $$( 1 + 481608 T + 9095120158391 T^{2} )^{2}$$
$73$ $$1 - 19886077213490 T^{2} +$$$$12\!\cdots\!09$$$$T^{4}$$
$79$ $$( 1 + 1059760 T + 19203908986159 T^{2} )^{2}$$
$83$ $$1 - 47492314121570 T^{2} +$$$$73\!\cdots\!29$$$$T^{4}$$
$89$ $$( 1 - 5644170 T + 44231334895529 T^{2} )^{2}$$
$97$ $$1 - 17378330046530 T^{2} +$$$$65\!\cdots\!69$$$$T^{4}$$