Properties

Label 4.4.5725.1-41.1-b
Base field 4.4.5725.1
Weight $[2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$
Dimension $9$
CM no
Base change no

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Base field 4.4.5725.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$
Dimension: $9$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

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

\(x^{9} - 2x^{8} - 43x^{7} + 94x^{6} + 446x^{5} - 1101x^{4} - 616x^{3} + 2034x^{2} + 270x - 914\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ $\phantom{-}e$
9 $[9, 3, -w + 1]$ $-\frac{233667190}{12191019113}e^{8} + \frac{74359977}{12191019113}e^{7} + \frac{9996783760}{12191019113}e^{6} - \frac{4939271955}{12191019113}e^{5} - \frac{104955430794}{12191019113}e^{4} + \frac{69434522490}{12191019113}e^{3} + \frac{184011546248}{12191019113}e^{2} - \frac{24209839454}{12191019113}e - \frac{41841204404}{12191019113}$
11 $[11, 11, w]$ $\phantom{-}\frac{218071166}{12191019113}e^{8} - \frac{93936012}{12191019113}e^{7} - \frac{9220535706}{12191019113}e^{6} + \frac{5638060361}{12191019113}e^{5} + \frac{93730337924}{12191019113}e^{4} - \frac{74524367938}{12191019113}e^{3} - \frac{139529678404}{12191019113}e^{2} + \frac{20424327736}{12191019113}e + \frac{57592487710}{12191019113}$
11 $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ $-\frac{2342550}{1741574159}e^{8} + \frac{12248927}{1741574159}e^{7} + \frac{102426737}{1741574159}e^{6} - \frac{548462391}{1741574159}e^{5} - \frac{1057674089}{1741574159}e^{4} + \frac{6145350693}{1741574159}e^{3} + \frac{817893490}{1741574159}e^{2} - \frac{10031713225}{1741574159}e - \frac{347458392}{1741574159}$
11 $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ $\phantom{-}\frac{114260022}{12191019113}e^{8} + \frac{232846777}{12191019113}e^{7} - \frac{5366348823}{12191019113}e^{6} - \frac{8945052609}{12191019113}e^{5} + \frac{73320161160}{12191019113}e^{4} + \frac{76189119432}{12191019113}e^{3} - \frac{331085684898}{12191019113}e^{2} - \frac{49408931608}{12191019113}e + \frac{252342337700}{12191019113}$
11 $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ $-\frac{250065040}{12191019113}e^{8} + \frac{160102466}{12191019113}e^{7} + \frac{10713770919}{12191019113}e^{6} - \frac{8778508692}{12191019113}e^{5} - \frac{112359149417}{12191019113}e^{4} + \frac{112451977341}{12191019113}e^{3} + \frac{189736800678}{12191019113}e^{2} - \frac{106622851142}{12191019113}e - \frac{44273413148}{12191019113}$
16 $[16, 2, 2]$ $-\frac{57650961}{12191019113}e^{8} - \frac{325304508}{12191019113}e^{7} + \frac{2876519211}{12191019113}e^{6} + \frac{13154610958}{12191019113}e^{5} - \frac{45826310343}{12191019113}e^{4} - \frac{122696022356}{12191019113}e^{3} + \frac{274800109905}{12191019113}e^{2} + \frac{118075459812}{12191019113}e - \frac{213904251473}{12191019113}$
25 $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $-\frac{218962671}{12191019113}e^{8} + \frac{211702704}{12191019113}e^{7} + \frac{9193189186}{12191019113}e^{6} - \frac{10683284277}{12191019113}e^{5} - \frac{90030632533}{12191019113}e^{4} + \frac{126664421074}{12191019113}e^{3} + \frac{83056132921}{12191019113}e^{2} - \frac{95024724128}{12191019113}e - \frac{8367190254}{12191019113}$
29 $[29, 29, -w - 3]$ $\phantom{-}\frac{77130744}{12191019113}e^{8} - \frac{186196012}{12191019113}e^{7} - \frac{3187460910}{12191019113}e^{6} + \frac{8393291812}{12191019113}e^{5} + \frac{28307942095}{12191019113}e^{4} - \frac{88787516390}{12191019113}e^{3} + \frac{19346796822}{12191019113}e^{2} + \frac{61739536860}{12191019113}e - \frac{15047365156}{12191019113}$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $\phantom{-}\frac{235270842}{12191019113}e^{8} - \frac{284997025}{12191019113}e^{7} - \frac{9878261970}{12191019113}e^{6} + \frac{14015322241}{12191019113}e^{5} + \frac{97312682300}{12191019113}e^{4} - \frac{165649123088}{12191019113}e^{3} - \frac{106498319420}{12191019113}e^{2} + \frac{181464839394}{12191019113}e + \frac{78208188504}{12191019113}$
31 $[31, 31, w^{3} - 6w + 1]$ $\phantom{-}\frac{49818434}{1741574159}e^{8} + \frac{7595468}{1741574159}e^{7} - \frac{2186267384}{1741574159}e^{6} + \frac{76034927}{1741574159}e^{5} + \frac{24922031101}{1741574159}e^{4} - \frac{5907529051}{1741574159}e^{3} - \frac{68048659676}{1741574159}e^{2} + \frac{9374203847}{1741574159}e + \frac{44623862022}{1741574159}$
31 $[31, 31, w^{3} - 6w - 2]$ $\phantom{-}\frac{228963018}{12191019113}e^{8} - \frac{387784876}{12191019113}e^{7} - \frac{9418103386}{12191019113}e^{6} + \frac{18003605390}{12191019113}e^{5} + \frac{84092542452}{12191019113}e^{4} - \frac{196506366016}{12191019113}e^{3} + \frac{41728778869}{12191019113}e^{2} + \frac{144280510022}{12191019113}e - \frac{126095586404}{12191019113}$
41 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $-1$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $\phantom{-}\frac{327601914}{12191019113}e^{8} - \frac{804649017}{12191019113}e^{7} - \frac{13654253719}{12191019113}e^{6} + \frac{36159817168}{12191019113}e^{5} + \frac{126743952354}{12191019113}e^{4} - \frac{384125796192}{12191019113}e^{3} + \frac{2436684214}{12191019113}e^{2} + \frac{374233260214}{12191019113}e - \frac{46180692260}{12191019113}$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $-\frac{174257033}{12191019113}e^{8} - \frac{80111198}{12191019113}e^{7} + \frac{7605935815}{12191019113}e^{6} + \frac{1984018521}{12191019113}e^{5} - \frac{85872021161}{12191019113}e^{4} - \frac{27887612}{12191019113}e^{3} + \frac{227095086346}{12191019113}e^{2} - \frac{30016370255}{12191019113}e - \frac{74103391006}{12191019113}$
59 $[59, 59, w^{3} + w^{2} - 6w - 4]$ $\phantom{-}\frac{292861087}{12191019113}e^{8} - \frac{507669616}{12191019113}e^{7} - \frac{12372659437}{12191019113}e^{6} + \frac{23777303279}{12191019113}e^{5} + \frac{121228496582}{12191019113}e^{4} - \frac{268328831985}{12191019113}e^{3} - \frac{76402397748}{12191019113}e^{2} + \frac{320704660412}{12191019113}e - \frac{36560869570}{12191019113}$
79 $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $\phantom{-}\frac{449427842}{12191019113}e^{8} + \frac{128496427}{12191019113}e^{7} - \frac{19773506796}{12191019113}e^{6} - \frac{2502780526}{12191019113}e^{5} + \frac{227378973379}{12191019113}e^{4} - \frac{4048236715}{12191019113}e^{3} - \frac{642746892782}{12191019113}e^{2} - \frac{115090562662}{12191019113}e + \frac{449803549024}{12191019113}$
79 $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ $-\frac{25351070}{12191019113}e^{8} - \frac{25990779}{12191019113}e^{7} + \frac{1227481158}{12191019113}e^{6} + \frac{1337868995}{12191019113}e^{5} - \frac{17217402795}{12191019113}e^{4} - \frac{21811876760}{12191019113}e^{3} + \frac{72805980906}{12191019113}e^{2} + \frac{105439752780}{12191019113}e - \frac{78415323340}{12191019113}$
89 $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ $-\frac{116695751}{12191019113}e^{8} + \frac{257641478}{12191019113}e^{7} + \frac{4761330979}{12191019113}e^{6} - \frac{11677791210}{12191019113}e^{5} - \frac{40167379674}{12191019113}e^{4} + \frac{126700887581}{12191019113}e^{3} - \frac{65421955628}{12191019113}e^{2} - \frac{156255745602}{12191019113}e + \frac{195018630860}{12191019113}$
89 $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ $-\frac{14178498}{1741574159}e^{8} + \frac{38568019}{1741574159}e^{7} + \frac{629564487}{1741574159}e^{6} - \frac{1679450001}{1741574159}e^{5} - \frac{6916466692}{1741574159}e^{4} + \frac{17121790593}{1741574159}e^{3} + \frac{11191894978}{1741574159}e^{2} - \frac{17177169072}{1741574159}e - \frac{11750191424}{1741574159}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $1$