Properties

Label 4.4.19429.1-25.1-f
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 25, -2w^{3} + 5w^{2} + 6w - 5]$
Dimension $13$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 25, -2w^{3} + 5w^{2} + 6w - 5]$
Dimension: $13$
CM: no
Base change: no
Newspace dimension: $53$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{13} + 4x^{12} - 22x^{11} - 94x^{10} + 172x^{9} + 821x^{8} - 546x^{7} - 3266x^{6} + 465x^{5} + 5640x^{4} + 331x^{3} - 2877x^{2} + 541x - 15\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e$
5 $[5, 5, w]$ $\phantom{-}0$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $-\frac{337186}{477831}e^{12} - \frac{251225}{159277}e^{11} + \frac{8725192}{477831}e^{10} + \frac{5398723}{159277}e^{9} - \frac{86197495}{477831}e^{8} - \frac{122753902}{477831}e^{7} + \frac{398998948}{477831}e^{6} + \frac{384385510}{477831}e^{5} - \frac{834950191}{477831}e^{4} - \frac{396946838}{477831}e^{3} + \frac{598699402}{477831}e^{2} - \frac{107312434}{477831}e + \frac{1028351}{159277}$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{2071466}{2389155}e^{12} - \frac{1482864}{796385}e^{11} + \frac{54129566}{2389155}e^{10} + \frac{31796999}{796385}e^{9} - \frac{540248756}{2389155}e^{8} - \frac{719292989}{2389155}e^{7} + \frac{2526373979}{2389155}e^{6} + \frac{2223682808}{2389155}e^{5} - \frac{5342108696}{2389155}e^{4} - \frac{2187728008}{2389155}e^{3} + \frac{775157050}{477831}e^{2} - \frac{827993768}{2389155}e + \frac{1921428}{159277}$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}\frac{47803}{28785}e^{12} + \frac{35702}{9595}e^{11} - \frac{1238818}{28785}e^{10} - \frac{770687}{9595}e^{9} + \frac{12250438}{28785}e^{8} + \frac{17641567}{28785}e^{7} - \frac{56701642}{28785}e^{6} - \frac{55859914}{28785}e^{5} + \frac{118387363}{28785}e^{4} + \frac{59253614}{28785}e^{3} - \frac{16840271}{5757}e^{2} + \frac{13622359}{28785}e - \frac{25183}{1919}$
16 $[16, 2, 2]$ $\phantom{-}\frac{915232}{2389155}e^{12} + \frac{670793}{796385}e^{11} - \frac{23846047}{2389155}e^{10} - \frac{14453548}{796385}e^{9} + \frac{237322582}{2389155}e^{8} + \frac{329355043}{2389155}e^{7} - \frac{1107492028}{2389155}e^{6} - \frac{1031423266}{2389155}e^{5} + \frac{2342184232}{2389155}e^{4} + \frac{1055111201}{2389155}e^{3} - \frac{342446726}{477831}e^{2} + \frac{313309591}{2389155}e - \frac{336094}{159277}$
17 $[17, 17, -w + 2]$ $-\frac{110438}{796385}e^{12} - \frac{289131}{796385}e^{11} + \frac{2726928}{796385}e^{10} + \frac{6319776}{796385}e^{9} - \frac{25334658}{796385}e^{8} - \frac{49474342}{796385}e^{7} + \frac{107830387}{796385}e^{6} + \frac{166295054}{796385}e^{5} - \frac{198100053}{796385}e^{4} - \frac{214860044}{796385}e^{3} + \frac{22097541}{159277}e^{2} + \frac{34860376}{796385}e - \frac{736642}{159277}$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{3940252}{2389155}e^{12} + \frac{2954753}{796385}e^{11} - \frac{101986807}{2389155}e^{10} - \frac{63782788}{796385}e^{9} + \frac{1007218792}{2389155}e^{8} + \frac{1460783938}{2389155}e^{7} - \frac{4655470453}{2389155}e^{6} - \frac{4636224406}{2389155}e^{5} + \frac{9704288647}{2389155}e^{4} + \frac{4977116036}{2389155}e^{3} - \frac{1378488044}{477831}e^{2} + \frac{1000145476}{2389155}e - \frac{537197}{159277}$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $-\frac{1102676}{796385}e^{12} - \frac{2432157}{796385}e^{11} + \frac{28678896}{796385}e^{10} + \frac{52395167}{796385}e^{9} - \frac{284735276}{796385}e^{8} - \frac{398181009}{796385}e^{7} + \frac{1323617569}{796385}e^{6} + \frac{1249604498}{796385}e^{5} - \frac{2776704246}{796385}e^{4} - \frac{1286264833}{796385}e^{3} + \frac{396797680}{159277}e^{2} - \frac{376154383}{796385}e + \frac{3438584}{159277}$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $-\frac{915232}{2389155}e^{12} - \frac{670793}{796385}e^{11} + \frac{23846047}{2389155}e^{10} + \frac{14453548}{796385}e^{9} - \frac{237322582}{2389155}e^{8} - \frac{329355043}{2389155}e^{7} + \frac{1107492028}{2389155}e^{6} + \frac{1031423266}{2389155}e^{5} - \frac{2342184232}{2389155}e^{4} - \frac{1055111201}{2389155}e^{3} + \frac{342924557}{477831}e^{2} - \frac{315698746}{2389155}e - \frac{460291}{159277}$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-\frac{224312}{159277}e^{12} - \frac{500219}{159277}e^{11} + \frac{5814948}{159277}e^{10} + \frac{10765872}{159277}e^{9} - \frac{57577672}{159277}e^{8} - \frac{81792265}{159277}e^{7} + \frac{267294468}{159277}e^{6} + \frac{257185861}{159277}e^{5} - \frac{561455694}{159277}e^{4} - \frac{268213415}{159277}e^{3} + \frac{404494240}{159277}e^{2} - \frac{68912022}{159277}e + \frac{1275881}{159277}$
41 $[41, 41, w^{2} - w - 1]$ $-\frac{1527133}{796385}e^{12} - \frac{3321176}{796385}e^{11} + \frac{39850418}{796385}e^{10} + \frac{71467866}{796385}e^{9} - \frac{397074043}{796385}e^{8} - \frac{541985142}{796385}e^{7} + \frac{1852986047}{796385}e^{6} + \frac{1693947854}{796385}e^{5} - \frac{3905930743}{796385}e^{4} - \frac{1725321864}{796385}e^{3} + \frac{563188378}{159277}e^{2} - \frac{534231339}{796385}e + \frac{3911148}{159277}$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{127760}{159277}e^{12} - \frac{295552}{159277}e^{11} + \frac{3299981}{159277}e^{10} + \frac{6439277}{159277}e^{9} - \frac{32519686}{159277}e^{8} - \frac{49851210}{159277}e^{7} + \frac{150003712}{159277}e^{6} + \frac{161784755}{159277}e^{5} - \frac{312041838}{159277}e^{4} - \frac{181984469}{159277}e^{3} + \frac{220582152}{159277}e^{2} - \frac{24815063}{159277}e - \frac{492561}{159277}$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-\frac{2205}{8383}e^{12} - \frac{4492}{8383}e^{11} + \frac{58688}{8383}e^{10} + \frac{98570}{8383}e^{9} - \frac{592941}{8383}e^{8} - \frac{769675}{8383}e^{7} + \frac{2775087}{8383}e^{6} + \frac{2533936}{8383}e^{5} - \frac{5758667}{8383}e^{4} - \frac{2964476}{8383}e^{3} + \frac{3941120}{8383}e^{2} - \frac{300410}{8383}e - \frac{33821}{8383}$
53 $[53, 53, -w - 3]$ $\phantom{-}\frac{128512}{796385}e^{12} + \frac{226739}{796385}e^{11} - \frac{3501202}{796385}e^{10} - \frac{4803384}{796385}e^{9} + \frac{36420427}{796385}e^{8} + \frac{35174493}{796385}e^{7} - \frac{177126413}{796385}e^{6} - \frac{100585086}{796385}e^{5} + \frac{389119247}{796385}e^{4} + \frac{66868221}{796385}e^{3} - \frac{59137770}{159277}e^{2} + \frac{102718561}{796385}e - \frac{96692}{159277}$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $-\frac{873793}{796385}e^{12} - \frac{1924276}{796385}e^{11} + \frac{22759798}{796385}e^{10} + \frac{41473526}{796385}e^{9} - \frac{226522583}{796385}e^{8} - \frac{315311877}{796385}e^{7} + \frac{1057560047}{796385}e^{6} + \frac{989144029}{796385}e^{5} - \frac{2237043723}{796385}e^{4} - \frac{1012300439}{796385}e^{3} + \frac{325335554}{159277}e^{2} - \frac{310460484}{796385}e + \frac{2614447}{159277}$
59 $[59, 59, 2w^{2} - 3w - 6]$ $\phantom{-}\frac{534564}{159277}e^{12} + \frac{1175609}{159277}e^{11} - \frac{13891849}{159277}e^{10} - \frac{25224009}{159277}e^{9} + \frac{137919269}{159277}e^{8} + \frac{190542232}{159277}e^{7} - \frac{642075074}{159277}e^{6} - \frac{591991673}{159277}e^{5} + \frac{1353238992}{159277}e^{4} + \frac{594585492}{159277}e^{3} - \frac{980224521}{159277}e^{2} + \frac{194908085}{159277}e - \frac{7712372}{159277}$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $-\frac{2525529}{796385}e^{12} - \frac{5628888}{796385}e^{11} + \frac{65542639}{796385}e^{10} + \frac{121430033}{796385}e^{9} - \frac{649333724}{796385}e^{8} - \frac{925536991}{796385}e^{7} + \frac{3012738526}{796385}e^{6} + \frac{2924570702}{796385}e^{5} - \frac{6312046539}{796385}e^{4} - \frac{3083528622}{796385}e^{3} + \frac{902994084}{159277}e^{2} - \frac{745923852}{796385}e + \frac{4478967}{159277}$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}\frac{1259506}{477831}e^{12} + \frac{917058}{159277}e^{11} - \frac{32820862}{477831}e^{10} - \frac{19732600}{159277}e^{9} + \frac{326567356}{477831}e^{8} + \frac{449012809}{477831}e^{7} - \frac{1522130143}{477831}e^{6} - \frac{1404606025}{477831}e^{5} + \frac{3207043903}{477831}e^{4} + \frac{1437276110}{477831}e^{3} - \frac{2317584091}{477831}e^{2} + \frac{424849330}{477831}e - \frac{3634689}{159277}$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}\frac{9063617}{2389155}e^{12} + \frac{6635893}{796385}e^{11} - \frac{235666547}{2389155}e^{10} - \frac{142495283}{796385}e^{9} + \frac{2340630842}{2389155}e^{8} + \frac{3233363993}{2389155}e^{7} - \frac{10897888928}{2389155}e^{6} - \frac{10069189721}{2389155}e^{5} + \frac{22959591857}{2389155}e^{4} + \frac{10176253351}{2389155}e^{3} - \frac{3321135847}{477831}e^{2} + \frac{3248304536}{2389155}e - \frac{7734885}{159277}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $-1$