# Properties

 Label 5.22.b Level $5$ Weight $22$ Character orbit 5.b Rep. character $\chi_{5}(4,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $1$ Sturm bound $11$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5$$ Weight: $$k$$ $$=$$ $$22$$ 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: $$11$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{22}(5, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 10 10 0
Eisenstein series 2 2 0

## Trace form

 $$10 q - 9273720 q^{4} - 25175970 q^{5} + 190183320 q^{6} - 46796905530 q^{9} + O(q^{10})$$ $$10 q - 9273720 q^{4} - 25175970 q^{5} + 190183320 q^{6} - 46796905530 q^{9} + 42469996280 q^{10} + 150626450520 q^{11} + 1196972791560 q^{14} + 28918735560 q^{15} + 13236859984160 q^{16} - 111339219544600 q^{19} + 210425436114840 q^{20} + 153512457036120 q^{21} - 925398618703200 q^{24} + 233060326559650 q^{25} - 621077824626480 q^{26} - 2607858467637300 q^{29} - 2586594238552440 q^{30} + 2526078405859520 q^{31} + 72842119718695360 q^{34} - 39547684375393320 q^{35} - 37582575203847240 q^{36} - 96095316750417360 q^{39} + 147883293047082400 q^{40} + 178989482851615620 q^{41} - 740313984960721440 q^{44} - 170779831343975790 q^{45} + 310308437385662920 q^{46} + 337573187662879630 q^{49} - 330613273664391600 q^{50} + 425405951744829120 q^{51} + 2276512248592508400 q^{54} - 4016119665475835640 q^{55} + 9526915367282527200 q^{56} + 1994566040408748600 q^{59} - 20957050062416020320 q^{60} + 5353281898917000620 q^{61} - 53705514970438977920 q^{64} - 12495942066653666640 q^{65} + 130803500735066708640 q^{66} - 100469090770094966760 q^{69} - 72656118333436657320 q^{70} + 148239232001721288720 q^{71} + 15604199347531682160 q^{74} - 355998150662931493200 q^{75} + 574798946837845274400 q^{76} - 190143330869910604000 q^{79} - 801735065581038901920 q^{80} + 1042969689596090972610 q^{81} - 984178622121811230240 q^{84} - 881984388527483667520 q^{85} + 2442532998478428470520 q^{86} - 1194549181591936131900 q^{89} - 2604678167917323770040 q^{90} + 2759667106510781727120 q^{91} - 2807277590161309874840 q^{94} - 1062907495565755235400 q^{95} + 9073487122609823752320 q^{96} - 2282448445798673329560 q^{99} + O(q^{100})$$

## Decomposition of $$S_{22}^{\mathrm{new}}(5, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5.22.b.a $10$ $13.974$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$-25175970$$ $$0$$ $$q+\beta _{1}q^{2}+(-6\beta _{1}-\beta _{4})q^{3}+(-927372+\cdots)q^{4}+\cdots$$