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 $0$

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