Properties

Label 4.4.14272.1-23.1-e
Base field 4.4.14272.1
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23, 23, w^{2} - 2w - 1]$
Dimension $11$
CM no
Base change no

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Base field 4.4.14272.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[23, 23, w^{2} - 2w - 1]$
Dimension: $11$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{11} + 6x^{10} - 4x^{9} - 82x^{8} - 90x^{7} + 290x^{6} + 517x^{5} - 222x^{4} - 707x^{3} - 124x^{2} + 134x - 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $\phantom{-}\frac{2432}{3427}e^{10} + \frac{14591}{3427}e^{9} - \frac{8036}{3427}e^{8} - \frac{193756}{3427}e^{7} - \frac{240608}{3427}e^{6} + \frac{625611}{3427}e^{5} + \frac{1319304}{3427}e^{4} - \frac{231171}{3427}e^{3} - \frac{1705938}{3427}e^{2} - \frac{653856}{3427}e + \frac{197960}{3427}$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $-\frac{3003}{3427}e^{10} - \frac{18300}{3427}e^{9} + \frac{9376}{3427}e^{8} + \frac{244213}{3427}e^{7} + \frac{304720}{3427}e^{6} - \frac{801576}{3427}e^{5} - \frac{1656914}{3427}e^{4} + \frac{354580}{3427}e^{3} + \frac{2125630}{3427}e^{2} + \frac{756283}{3427}e - \frac{227292}{3427}$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}\frac{1320}{3427}e^{10} + \frac{7818}{3427}e^{9} - \frac{4046}{3427}e^{8} - \frac{102413}{3427}e^{7} - \frac{134922}{3427}e^{6} + \frac{316866}{3427}e^{5} + \frac{730950}{3427}e^{4} - \frac{63368}{3427}e^{3} - \frac{935322}{3427}e^{2} - \frac{397997}{3427}e + \frac{102846}{3427}$
13 $[13, 13, -w + 2]$ $\phantom{-}\frac{97}{3427}e^{10} + \frac{3799}{3427}e^{9} + \frac{12232}{3427}e^{8} - \frac{44540}{3427}e^{7} - \frac{188477}{3427}e^{6} + \frac{79659}{3427}e^{5} + \frac{762246}{3427}e^{4} + \frac{254570}{3427}e^{3} - \frac{913690}{3427}e^{2} - \frac{500493}{3427}e + \frac{125462}{3427}$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $\phantom{-}\frac{3575}{3427}e^{10} + \frac{20317}{3427}e^{9} - \frac{16384}{3427}e^{8} - \frac{272942}{3427}e^{7} - \frac{289163}{3427}e^{6} + \frac{915581}{3427}e^{5} + \frac{1685791}{3427}e^{4} - \frac{491475}{3427}e^{3} - \frac{2196461}{3427}e^{2} - \frac{730782}{3427}e + \frac{231420}{3427}$
19 $[19, 19, -w^{2} + w + 4]$ $-\frac{4166}{3427}e^{10} - \frac{24456}{3427}e^{9} + \frac{17993}{3427}e^{8} + \frac{330922}{3427}e^{7} + \frac{350023}{3427}e^{6} - \frac{1134044}{3427}e^{5} - \frac{1996779}{3427}e^{4} + \frac{706400}{3427}e^{3} + \frac{2558046}{3427}e^{2} + \frac{766078}{3427}e - \frac{257014}{3427}$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}\frac{1452}{3427}e^{10} + \frac{10656}{3427}e^{9} + \frac{1718}{3427}e^{8} - \frac{140413}{3427}e^{7} - \frac{235460}{3427}e^{6} + \frac{441767}{3427}e^{5} + \frac{1143318}{3427}e^{4} - \frac{116312}{3427}e^{3} - \frac{1420903}{3427}e^{2} - \frac{526556}{3427}e + \frac{154940}{3427}$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}1$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $\phantom{-}\frac{20}{23}e^{10} + \frac{108}{23}e^{9} - \frac{108}{23}e^{8} - \frac{1451}{23}e^{7} - \frac{1394}{23}e^{6} + \frac{4870}{23}e^{5} + \frac{8614}{23}e^{4} - \frac{2621}{23}e^{3} - \frac{11468}{23}e^{2} - \frac{3893}{23}e + \frac{1276}{23}$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $-\frac{254}{149}e^{10} - \frac{1587}{149}e^{9} + \frac{630}{149}e^{8} + \frac{21057}{149}e^{7} + \frac{28074}{149}e^{6} - \frac{67782}{149}e^{5} - \frac{149071}{149}e^{4} + \frac{24072}{149}e^{3} + \frac{190326}{149}e^{2} + \frac{72622}{149}e - \frac{22468}{149}$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $\phantom{-}\frac{5214}{3427}e^{10} + \frac{36707}{3427}e^{9} + \frac{1496}{3427}e^{8} - \frac{483181}{3427}e^{7} - \frac{780714}{3427}e^{6} + \frac{1511730}{3427}e^{5} + \frac{3862234}{3427}e^{4} - \frac{336664}{3427}e^{3} - \frac{4840168}{3427}e^{2} - \frac{1923527}{3427}e + \frac{546406}{3427}$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{198}{149}e^{10} - \frac{1128}{149}e^{9} + \frac{890}{149}e^{8} + \frac{15131}{149}e^{7} + \frac{16260}{149}e^{6} - \frac{50495}{149}e^{5} - \frac{94370}{149}e^{4} + \frac{25776}{149}e^{3} + \frac{123208}{149}e^{2} + \frac{42870}{149}e - \frac{13922}{149}$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $-\frac{7473}{3427}e^{10} - \frac{42438}{3427}e^{9} + \frac{33514}{3427}e^{8} + \frac{566798}{3427}e^{7} + \frac{612852}{3427}e^{6} - \frac{1866032}{3427}e^{5} - \frac{3541019}{3427}e^{4} + \frac{849558}{3427}e^{3} + \frac{4582491}{3427}e^{2} + \frac{1717184}{3427}e - \frac{498770}{3427}$
59 $[59, 59, w - 4]$ $-\frac{17056}{3427}e^{10} - \frac{106252}{3427}e^{9} + \frac{45716}{3427}e^{8} + \frac{1414936}{3427}e^{7} + \frac{1835324}{3427}e^{6} - \frac{4606972}{3427}e^{5} - \frac{9804595}{3427}e^{4} + \frac{1854410}{3427}e^{3} + \frac{12512062}{3427}e^{2} + \frac{4609404}{3427}e - \frac{1394818}{3427}$
67 $[67, 67, 2w^{2} - 3w - 8]$ $\phantom{-}\frac{3815}{3427}e^{10} + \frac{18623}{3427}e^{9} - \frac{29893}{3427}e^{8} - \frac{256981}{3427}e^{7} - \frac{130194}{3427}e^{6} + \frac{935496}{3427}e^{5} + \frac{1078459}{3427}e^{4} - \frac{818592}{3427}e^{3} - \frac{1454626}{3427}e^{2} - \frac{285045}{3427}e + \frac{118024}{3427}$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $\phantom{-}\frac{7686}{3427}e^{10} + \frac{45304}{3427}e^{9} - \frac{31067}{3427}e^{8} - \frac{609735}{3427}e^{7} - \frac{678972}{3427}e^{6} + \frac{2054414}{3427}e^{5} + \frac{3839742}{3427}e^{4} - \frac{1127837}{3427}e^{3} - \frac{4969990}{3427}e^{2} - \frac{1630922}{3427}e + \frac{538124}{3427}$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $-\frac{13268}{3427}e^{10} - \frac{86496}{3427}e^{9} + \frac{21498}{3427}e^{8} + \frac{1147035}{3427}e^{7} + \frac{1627402}{3427}e^{6} - \frac{3684640}{3427}e^{5} - \frac{8412952}{3427}e^{4} + \frac{1276568}{3427}e^{3} + \frac{10647772}{3427}e^{2} + \frac{3971738}{3427}e - \frac{1199438}{3427}$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $-\frac{13011}{3427}e^{10} - \frac{86111}{3427}e^{9} + \frac{14443}{3427}e^{8} + \frac{1134840}{3427}e^{7} + \frac{1691123}{3427}e^{6} - \frac{3566573}{3427}e^{5} - \frac{8634757}{3427}e^{4} + \frac{870977}{3427}e^{3} + \frac{10932316}{3427}e^{2} + \frac{4402398}{3427}e - \frac{1275230}{3427}$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $-\frac{5195}{3427}e^{10} - \frac{34585}{3427}e^{9} + \frac{3903}{3427}e^{8} + \frac{453930}{3427}e^{7} + \frac{704297}{3427}e^{6} - \frac{1407272}{3427}e^{5} - \frac{3580123}{3427}e^{4} + \frac{258634}{3427}e^{3} + \frac{4542560}{3427}e^{2} + \frac{1855876}{3427}e - \frac{524940}{3427}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, w^{2} - 2w - 1]$ $-1$