# Properties

 Label 6.5.b Level 6 Weight 5 Character orbit b Rep. character $$\chi_{6}(5,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 1 Sturm bound 5 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$6 = 2 \cdot 3$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 6.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$5$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(6, [\chi])$$.

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

## Trace form

 $$2q - 6q^{3} - 16q^{4} + 48q^{6} + 52q^{7} - 126q^{9} + O(q^{10})$$ $$2q - 6q^{3} - 16q^{4} + 48q^{6} + 52q^{7} - 126q^{9} - 96q^{10} + 48q^{12} + 100q^{13} + 288q^{15} + 128q^{16} - 288q^{18} - 716q^{19} - 156q^{21} + 672q^{22} - 384q^{24} + 674q^{25} + 1242q^{27} - 416q^{28} + 288q^{30} - 1484q^{31} - 2016q^{33} - 1152q^{34} + 1008q^{36} + 3748q^{37} - 300q^{39} + 768q^{40} + 1248q^{42} - 524q^{43} - 1728q^{45} - 2112q^{46} - 384q^{48} - 3450q^{49} + 3456q^{51} - 800q^{52} - 2160q^{54} + 4032q^{55} + 2148q^{57} + 8160q^{58} - 2304q^{60} - 2972q^{61} - 3276q^{63} - 1024q^{64} - 2016q^{66} - 8972q^{67} + 6336q^{69} - 2496q^{70} + 2304q^{72} + 580q^{73} - 2022q^{75} + 5728q^{76} + 2400q^{78} + 19636q^{79} + 2754q^{81} - 13632q^{82} + 1248q^{84} - 6912q^{85} - 24480q^{87} - 5376q^{88} + 6048q^{90} + 2600q^{91} + 4452q^{93} + 9600q^{94} + 3072q^{96} - 956q^{97} + 12096q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(6, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
6.5.b.a $$2$$ $$0.620$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-6$$ $$0$$ $$52$$ $$q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 8 T^{2}$$
$3$ $$1 + 6 T + 81 T^{2}$$
$5$ $$1 - 962 T^{2} + 390625 T^{4}$$
$7$ $$( 1 - 26 T + 2401 T^{2} )^{2}$$
$11$ $$1 - 15170 T^{2} + 214358881 T^{4}$$
$13$ $$( 1 - 50 T + 28561 T^{2} )^{2}$$
$17$ $$1 - 125570 T^{2} + 6975757441 T^{4}$$
$19$ $$( 1 + 358 T + 130321 T^{2} )^{2}$$
$23$ $$1 - 420290 T^{2} + 78310985281 T^{4}$$
$29$ $$1 + 666238 T^{2} + 500246412961 T^{4}$$
$31$ $$( 1 + 742 T + 923521 T^{2} )^{2}$$
$37$ $$( 1 - 1874 T + 1874161 T^{2} )^{2}$$
$41$ $$1 + 155710 T^{2} + 7984925229121 T^{4}$$
$43$ $$( 1 + 262 T + 3418801 T^{2} )^{2}$$
$47$ $$1 - 6879362 T^{2} + 23811286661761 T^{4}$$
$53$ $$1 - 15571010 T^{2} + 62259690411361 T^{4}$$
$59$ $$1 - 20937410 T^{2} + 146830437604321 T^{4}$$
$61$ $$( 1 + 1486 T + 13845841 T^{2} )^{2}$$
$67$ $$( 1 + 4486 T + 20151121 T^{2} )^{2}$$
$71$ $$1 - 38122562 T^{2} + 645753531245761 T^{4}$$
$73$ $$( 1 - 290 T + 28398241 T^{2} )^{2}$$
$79$ $$( 1 - 9818 T + 38950081 T^{2} )^{2}$$
$83$ $$1 - 44355074 T^{2} + 2252292232139041 T^{4}$$
$89$ $$1 - 64012610 T^{2} + 3936588805702081 T^{4}$$
$97$ $$( 1 + 478 T + 88529281 T^{2} )^{2}$$