Properties

Base field 4.4.11525.1
Weight [2, 2, 2, 2]
Level norm 19
Level $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$
Label 4.4.11525.1-19.1-b
Dimension 10
CM no
Base change no

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Base field 4.4.11525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$
Label 4.4.11525.1-19.1-b
Dimension 10
Is CM no
Is base change no
Parent newspace dimension 16

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} \) \(\mathstrut -\mathstrut 5x^{9} \) \(\mathstrut -\mathstrut 18x^{8} \) \(\mathstrut +\mathstrut 98x^{7} \) \(\mathstrut +\mathstrut 105x^{6} \) \(\mathstrut -\mathstrut 621x^{5} \) \(\mathstrut -\mathstrut 177x^{4} \) \(\mathstrut +\mathstrut 1436x^{3} \) \(\mathstrut -\mathstrut 88x^{2} \) \(\mathstrut -\mathstrut 1088x \) \(\mathstrut +\mathstrut 304\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}\frac{36441}{845392}e^{9} - \frac{229385}{845392}e^{8} - \frac{175861}{422696}e^{7} + \frac{1973431}{422696}e^{6} - \frac{1253695}{845392}e^{5} - \frac{19641161}{845392}e^{4} + \frac{17755471}{845392}e^{3} + \frac{5445983}{211348}e^{2} - \frac{6891285}{211348}e + \frac{469192}{52837}$
11 $[11, 11, w + 1]$ $\phantom{-}\frac{26281}{845392}e^{9} - \frac{141565}{845392}e^{8} - \frac{192619}{422696}e^{7} + \frac{1271011}{422696}e^{6} + \frac{1354665}{845392}e^{5} - \frac{13712141}{845392}e^{4} + \frac{1277283}{845392}e^{3} + \frac{1328833}{52837}e^{2} - \frac{708833}{211348}e - \frac{294332}{52837}$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}\frac{10689}{422696}e^{9} - \frac{11163}{105674}e^{8} - \frac{236059}{422696}e^{7} + \frac{119092}{52837}e^{6} + \frac{1485911}{422696}e^{5} - \frac{1406563}{105674}e^{4} - \frac{945333}{211348}e^{3} + \frac{8139475}{422696}e^{2} - \frac{274975}{105674}e - \frac{20511}{105674}$
16 $[16, 2, 2]$ $-\frac{10201}{845392}e^{9} + \frac{10063}{845392}e^{8} + \frac{91057}{211348}e^{7} - \frac{96901}{422696}e^{6} - \frac{4512653}{845392}e^{5} + \frac{1100783}{845392}e^{4} + \frac{21020571}{845392}e^{3} - \frac{1823513}{422696}e^{2} - \frac{6966673}{211348}e + \frac{839171}{105674}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $-1$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $\phantom{-}\frac{946}{52837}e^{9} - \frac{8801}{52837}e^{8} + \frac{2247}{52837}e^{7} + \frac{173241}{52837}e^{6} - \frac{306103}{52837}e^{5} - \frac{969964}{52837}e^{4} + \frac{2145325}{52837}e^{3} + \frac{1122499}{52837}e^{2} - \frac{2878896}{52837}e + \frac{440022}{52837}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $-\frac{81}{105674}e^{9} - \frac{12121}{211348}e^{8} + \frac{65075}{211348}e^{7} + \frac{105083}{105674}e^{6} - \frac{301320}{52837}e^{5} - \frac{946601}{211348}e^{4} + \frac{6607773}{211348}e^{3} - \frac{145085}{211348}e^{2} - \frac{2205822}{52837}e + \frac{617049}{52837}$
19 $[19, 19, w - 1]$ $-\frac{3567}{52837}e^{9} + \frac{49391}{105674}e^{8} + \frac{43823}{105674}e^{7} - \frac{419368}{52837}e^{6} + \frac{355553}{52837}e^{5} + \frac{4063511}{105674}e^{4} - \frac{6027645}{105674}e^{3} - \frac{4025147}{105674}e^{2} + \frac{4438356}{52837}e - \frac{991932}{52837}$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}\frac{28145}{422696}e^{9} - \frac{222579}{422696}e^{8} - \frac{5907}{52837}e^{7} + \frac{1915769}{211348}e^{6} - \frac{5277931}{422696}e^{5} - \frac{18529283}{422696}e^{4} + \frac{37414185}{422696}e^{3} + \frac{7340803}{211348}e^{2} - \frac{13233919}{105674}e + \frac{2195969}{52837}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}\frac{5203}{211348}e^{9} + \frac{8863}{422696}e^{8} - \frac{503653}{422696}e^{7} + \frac{81015}{211348}e^{6} + \frac{1549091}{105674}e^{5} - \frac{2691217}{422696}e^{4} - \frac{25751183}{422696}e^{3} + \frac{10128335}{422696}e^{2} + \frac{3650046}{52837}e - \frac{2673459}{105674}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-\frac{14523}{422696}e^{9} + \frac{110035}{422696}e^{8} + \frac{7467}{211348}e^{7} - \frac{807377}{211348}e^{6} + \frac{1902677}{422696}e^{5} + \frac{6964787}{422696}e^{4} - \frac{10803773}{422696}e^{3} - \frac{2083121}{105674}e^{2} + \frac{3549371}{105674}e + \frac{20496}{52837}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}\frac{107263}{845392}e^{9} - \frac{734003}{845392}e^{8} - \frac{321921}{422696}e^{7} + \frac{5987141}{422696}e^{6} - \frac{9154129}{845392}e^{5} - \frac{56282259}{845392}e^{4} + \frac{74039421}{845392}e^{3} + \frac{7095089}{105674}e^{2} - \frac{26359447}{211348}e + \frac{1781137}{52837}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $\phantom{-}\frac{4567}{105674}e^{9} - \frac{94137}{211348}e^{8} + \frac{93411}{211348}e^{7} + \frac{804351}{105674}e^{6} - \frac{922503}{52837}e^{5} - \frac{7767649}{211348}e^{4} + \frac{22609605}{211348}e^{3} + \frac{5873723}{211348}e^{2} - \frac{7788800}{52837}e + \frac{1995395}{52837}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $-\frac{45765}{422696}e^{9} + \frac{247989}{422696}e^{8} + \frac{328437}{211348}e^{7} - \frac{2254019}{211348}e^{6} - \frac{1542245}{422696}e^{5} + \frac{23690669}{422696}e^{4} - \frac{9942275}{422696}e^{3} - \frac{7571755}{105674}e^{2} + \frac{5932607}{105674}e - \frac{36088}{52837}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $\phantom{-}\frac{17715}{422696}e^{9} - \frac{66899}{422696}e^{8} - \frac{206311}{211348}e^{7} + \frac{631157}{211348}e^{6} + \frac{3669875}{422696}e^{5} - \frac{7185835}{422696}e^{4} - \frac{13226683}{422696}e^{3} + \frac{3245935}{105674}e^{2} + \frac{3326805}{105674}e - \frac{534074}{52837}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $\phantom{-}\frac{36579}{422696}e^{9} - \frac{158395}{422696}e^{8} - \frac{378723}{211348}e^{7} + \frac{1615817}{211348}e^{6} + \frac{4528355}{422696}e^{5} - \frac{18601923}{422696}e^{4} - \frac{5327195}{422696}e^{3} + \frac{6823735}{105674}e^{2} - \frac{902707}{105674}e - \frac{530878}{52837}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $-\frac{7715}{52837}e^{9} + \frac{165231}{211348}e^{8} + \frac{432393}{211348}e^{7} - \frac{1429593}{105674}e^{6} - \frac{618443}{105674}e^{5} + \frac{14207879}{211348}e^{4} - \frac{3858855}{211348}e^{3} - \frac{16601387}{211348}e^{2} + \frac{2426162}{52837}e - \frac{241389}{52837}$
71 $[71, 71, w^{2} - 8]$ $-\frac{10025}{211348}e^{9} + \frac{26945}{105674}e^{8} + \frac{132409}{211348}e^{7} - \frac{205662}{52837}e^{6} - \frac{772711}{211348}e^{5} + \frac{2033599}{105674}e^{4} + \frac{731995}{52837}e^{3} - \frac{8177545}{211348}e^{2} - \frac{697468}{52837}e + \frac{1213445}{52837}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $\phantom{-}\frac{13809}{105674}e^{9} - \frac{125351}{211348}e^{8} - \frac{511027}{211348}e^{7} + \frac{1145753}{105674}e^{6} + \frac{751634}{52837}e^{5} - \frac{11825659}{211348}e^{4} - \frac{5231341}{211348}e^{3} + \frac{14080801}{211348}e^{2} + \frac{603822}{52837}e + \frac{196775}{52837}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $1$