Properties

Label 5.5.160801.1-27.1-e
Base field 5.5.160801.1
Weight $[2, 2, 2, 2, 2]$
Level norm $27$
Level $[27, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$
Dimension $9$
CM no
Base change no

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Base field 5.5.160801.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[27, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$
Dimension: $9$
CM: no
Base change: no
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

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

\(x^{9} - 4x^{8} - 54x^{7} + 258x^{6} + 648x^{5} - 4516x^{4} + 2280x^{3} + 17256x^{2} - 27184x + 9680\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}1$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-1$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}e$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}\frac{381419}{80974643}e^{8} - \frac{1050003}{80974643}e^{7} - \frac{45021663}{161949286}e^{6} + \frac{138038499}{161949286}e^{5} + \frac{731886831}{161949286}e^{4} - \frac{1230296568}{80974643}e^{3} - \frac{1184569222}{80974643}e^{2} + \frac{5102684074}{80974643}e - \frac{2035744288}{80974643}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $-\frac{3721627}{323898572}e^{8} + \frac{1623847}{80974643}e^{7} + \frac{107168797}{161949286}e^{6} - \frac{240139299}{161949286}e^{5} - \frac{1714788127}{161949286}e^{4} + \frac{2295748533}{80974643}e^{3} + \frac{2788714909}{80974643}e^{2} - \frac{9893512164}{80974643}e + \frac{4545784174}{80974643}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{2734525}{323898572}e^{8} - \frac{950765}{80974643}e^{7} - \frac{158522455}{323898572}e^{6} + \frac{144918835}{161949286}e^{5} + \frac{645524051}{80974643}e^{4} - \frac{1393790093}{80974643}e^{3} - \frac{2314783386}{80974643}e^{2} + \frac{5903260760}{80974643}e - \frac{2048467720}{80974643}$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}\frac{80125}{323898572}e^{8} - \frac{192127}{323898572}e^{7} - \frac{2641657}{323898572}e^{6} + \frac{4407344}{80974643}e^{5} - \frac{3388326}{80974643}e^{4} - \frac{98480951}{80974643}e^{3} + \frac{160813814}{80974643}e^{2} + \frac{536250954}{80974643}e - \frac{365652138}{80974643}$
31 $[31, 31, w^{3} - 4w + 2]$ $-\frac{3137161}{647797144}e^{8} + \frac{3064395}{323898572}e^{7} + \frac{90780243}{323898572}e^{6} - \frac{222840345}{323898572}e^{5} - \frac{361861780}{80974643}e^{4} + \frac{1070038766}{80974643}e^{3} + \frac{1073158857}{80974643}e^{2} - \frac{4802162928}{80974643}e + \frac{2656754536}{80974643}$
32 $[32, 2, 2]$ $-\frac{1767967}{161949286}e^{8} + \frac{11624257}{647797144}e^{7} + \frac{202386281}{323898572}e^{6} - \frac{216414305}{161949286}e^{5} - \frac{3189559593}{323898572}e^{4} + \frac{4118584157}{161949286}e^{3} + \frac{2416376177}{80974643}e^{2} - \frac{8599545360}{80974643}e + \frac{4575259164}{80974643}$
37 $[37, 37, w^{3} - 3w - 1]$ $-\frac{9035721}{647797144}e^{8} + \frac{2143729}{80974643}e^{7} + \frac{130846861}{161949286}e^{6} - \frac{608781739}{323898572}e^{5} - \frac{2090539129}{161949286}e^{4} + \frac{2836892247}{80974643}e^{3} + \frac{3287504798}{80974643}e^{2} - \frac{12005126474}{80974643}e + \frac{5651072524}{80974643}$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $\phantom{-}\frac{5070109}{323898572}e^{8} - \frac{8593925}{323898572}e^{7} - \frac{293062513}{323898572}e^{6} + \frac{318441123}{161949286}e^{5} + \frac{2363843949}{161949286}e^{4} - \frac{3046089624}{80974643}e^{3} - \frac{4042628022}{80974643}e^{2} + \frac{12966976894}{80974643}e - \frac{4620209038}{80974643}$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}\frac{477337}{80974643}e^{8} - \frac{1050592}{80974643}e^{7} - \frac{27876793}{80974643}e^{6} + \frac{145530643}{161949286}e^{5} + \frac{451098947}{80974643}e^{4} - \frac{2677223059}{161949286}e^{3} - \frac{1440092416}{80974643}e^{2} + \frac{5612265634}{80974643}e - \frac{3070725730}{80974643}$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $\phantom{-}\frac{899159}{161949286}e^{8} - \frac{949801}{323898572}e^{7} - \frac{25438165}{80974643}e^{6} + \frac{28181802}{80974643}e^{5} + \frac{416926355}{80974643}e^{4} - \frac{631429655}{80974643}e^{3} - \frac{1754959296}{80974643}e^{2} + \frac{2842123135}{80974643}e - \frac{22096124}{80974643}$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}\frac{92093}{161949286}e^{8} + \frac{1347633}{161949286}e^{7} - \frac{11591373}{323898572}e^{6} - \frac{76655315}{161949286}e^{5} + \frac{71242394}{80974643}e^{4} + \frac{631572826}{80974643}e^{3} - \frac{768350838}{80974643}e^{2} - \frac{2622107446}{80974643}e + \frac{2764718154}{80974643}$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-\frac{1235107}{161949286}e^{8} + \frac{6306199}{323898572}e^{7} + \frac{144289425}{323898572}e^{6} - \frac{106379731}{80974643}e^{5} - \frac{577669983}{80974643}e^{4} + \frac{1926881968}{80974643}e^{3} + \frac{1707246362}{80974643}e^{2} - \frac{7989117252}{80974643}e + \frac{4447533736}{80974643}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}\frac{4626929}{323898572}e^{8} - \frac{6288207}{323898572}e^{7} - \frac{131997267}{161949286}e^{6} + \frac{248342179}{161949286}e^{5} + \frac{2096861683}{161949286}e^{4} - \frac{4898816095}{161949286}e^{3} - \frac{3421617422}{80974643}e^{2} + \frac{10801732887}{80974643}e - \frac{5184772590}{80974643}$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $\phantom{-}\frac{1159293}{323898572}e^{8} - \frac{953412}{80974643}e^{7} - \frac{66637123}{323898572}e^{6} + \frac{122772825}{161949286}e^{5} + \frac{249610301}{80974643}e^{4} - \frac{1069648788}{80974643}e^{3} - \frac{422239695}{80974643}e^{2} + \frac{4186135964}{80974643}e - \frac{2871791858}{80974643}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{2427677}{161949286}e^{8} + \frac{1721616}{80974643}e^{7} + \frac{280671489}{323898572}e^{6} - \frac{270389261}{161949286}e^{5} - \frac{1144038241}{80974643}e^{4} + \frac{2673026236}{80974643}e^{3} + \frac{4143065467}{80974643}e^{2} - \frac{11748248751}{80974643}e + \frac{3998257342}{80974643}$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $\phantom{-}\frac{5808169}{323898572}e^{8} - \frac{12799231}{323898572}e^{7} - \frac{337163173}{323898572}e^{6} + \frac{445406617}{161949286}e^{5} + \frac{1349908515}{80974643}e^{4} - \frac{8228631079}{161949286}e^{3} - \frac{4240438077}{80974643}e^{2} + \frac{17454022499}{80974643}e - \frac{7958336468}{80974643}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-\frac{2659403}{323898572}e^{8} + \frac{1147772}{80974643}e^{7} + \frac{156377221}{323898572}e^{6} - \frac{168288461}{161949286}e^{5} - \frac{652587593}{80974643}e^{4} + \frac{1607574271}{80974643}e^{3} + \frac{2538919780}{80974643}e^{2} - \frac{6876446018}{80974643}e + \frac{1650166742}{80974643}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-1$
$9$ $[9, 3, -w^{4} + 5w^{2} - 3]$ $1$