Properties

Label 2.2.220.1-3.1-c
Base field \(\Q(\sqrt{55}) \)
Weight $[2, 2]$
Level norm $3$
Level $[3, 3, w + 1]$
Dimension $16$
CM no
Base change no

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Base field \(\Q(\sqrt{55}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[3, 3, w + 1]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} + 60x^{14} + 1346x^{12} + 14040x^{10} + 67921x^{8} + 129884x^{6} + 74064x^{4} + 13504x^{2} + 256\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}\frac{309706439}{197457236608}e^{15} + \frac{4608179083}{49364309152}e^{13} + \frac{203959158615}{98728618304}e^{11} + \frac{518614665811}{24682154576}e^{9} + \frac{18983190523319}{197457236608}e^{7} + \frac{7648327613915}{49364309152}e^{5} + \frac{385740600025}{12341077288}e^{3} - \frac{13299755859}{1542634661}e$
3 $[3, 3, w + 1]$ $-\frac{11523}{1313824}e^{15} - \frac{686685}{1313824}e^{13} - \frac{951877}{82114}e^{11} - \frac{9723097}{82114}e^{9} - \frac{719100509}{1313824}e^{7} - \frac{1202061251}{1313824}e^{5} - \frac{11145560}{41057}e^{3} + \frac{59629}{41057}e$
3 $[3, 3, w + 2]$ $-\frac{309706439}{197457236608}e^{15} - \frac{4608179083}{49364309152}e^{13} - \frac{203959158615}{98728618304}e^{11} - \frac{518614665811}{24682154576}e^{9} - \frac{18983190523319}{197457236608}e^{7} - \frac{7648327613915}{49364309152}e^{5} - \frac{385740600025}{12341077288}e^{3} + \frac{14842390520}{1542634661}e$
5 $[5, 5, -2w + 15]$ $-\frac{613193579}{98728618304}e^{14} - \frac{9144636301}{24682154576}e^{12} - \frac{406310234195}{49364309152}e^{10} - \frac{1040689053985}{12341077288}e^{8} - \frac{38733324226299}{98728618304}e^{6} - \frac{16508446158437}{24682154576}e^{4} - \frac{345272360250}{1542634661}e^{2} - \frac{9640594767}{1542634661}$
11 $[11, 11, 3w - 22]$ $\phantom{-}\frac{739098001}{493643091520}e^{14} + \frac{11048649721}{123410772880}e^{12} + \frac{492864465101}{246821545760}e^{10} + \frac{158939488012}{7713173305}e^{8} + \frac{48055823468073}{493643091520}e^{6} + \frac{21418363384359}{123410772880}e^{4} + \frac{1129134042769}{15426346610}e^{2} + \frac{38024452499}{7713173305}$
13 $[13, 13, w + 4]$ $\phantom{-}\frac{37559336411}{987286183040}e^{15} + \frac{69925647997}{30852693220}e^{13} + \frac{24802398249611}{493643091520}e^{11} + \frac{3955102905131}{7713173305}e^{9} + \frac{2335562296423083}{987286183040}e^{7} + \frac{121250306349703}{30852693220}e^{5} + \frac{68713781579563}{61705386440}e^{3} - \frac{179638820343}{7713173305}e$
13 $[13, 13, w + 9]$ $\phantom{-}\frac{19900248969}{987286183040}e^{15} + \frac{296626654249}{246821545760}e^{13} + \frac{13168913801609}{493643091520}e^{11} + \frac{33681272516329}{123410772880}e^{9} + \frac{1249771919509177}{987286183040}e^{7} + \frac{527925246430761}{246821545760}e^{5} + \frac{42094866345327}{61705386440}e^{3} + \frac{116306484003}{7713173305}e$
17 $[17, 17, w + 2]$ $-\frac{19900248969}{987286183040}e^{15} - \frac{296626654249}{246821545760}e^{13} - \frac{13168913801609}{493643091520}e^{11} - \frac{33681272516329}{123410772880}e^{9} - \frac{1249771919509177}{987286183040}e^{7} - \frac{527925246430761}{246821545760}e^{5} - \frac{42094866345327}{61705386440}e^{3} - \frac{116306484003}{7713173305}e$
17 $[17, 17, w + 15]$ $\phantom{-}\frac{30194153467}{493643091520}e^{15} + \frac{899990912019}{246821545760}e^{13} + \frac{19972822495387}{246821545760}e^{11} + \frac{102120577526919}{123410772880}e^{9} + \frac{1892814668116091}{493643091520}e^{7} + \frac{1594446324255451}{246821545760}e^{5} + \frac{15597431127649}{7713173305}e^{3} + \frac{215905589138}{7713173305}e$
19 $[19, 19, -w - 6]$ $-\frac{1348130443}{246821545760}e^{14} - \frac{20065153503}{61705386440}e^{12} - \frac{888635749153}{123410772880}e^{10} - \frac{4525560906431}{61705386440}e^{8} - \frac{83160808349639}{246821545760}e^{6} - \frac{4261344772794}{7713173305}e^{4} - \frac{2192535373039}{15426346610}e^{2} + \frac{20971276491}{7713173305}$
19 $[19, 19, w - 6]$ $-\frac{2291962289}{123410772880}e^{14} - \frac{34171642499}{30852693220}e^{12} - \frac{758827409637}{30852693220}e^{10} - \frac{15536822670301}{61705386440}e^{8} - \frac{144333491499947}{123410772880}e^{6} - \frac{122508809413287}{61705386440}e^{4} - \frac{10121470910839}{15426346610}e^{2} - \frac{161712757149}{7713173305}$
23 $[23, 23, w + 3]$ $\phantom{-}\frac{47077655}{1542634661}e^{15} + \frac{89779139831}{49364309152}e^{13} + \frac{497839792641}{12341077288}e^{11} + \frac{10171772451181}{24682154576}e^{9} + \frac{23514015560645}{12341077288}e^{7} + \frac{157278744005731}{49364309152}e^{5} + \frac{2907286492725}{3085269322}e^{3} - \frac{14345137561}{1542634661}e$
23 $[23, 23, w + 20]$ $-\frac{290131281}{49364309152}e^{15} - \frac{8629861611}{24682154576}e^{13} - \frac{190847892775}{24682154576}e^{11} - \frac{484751531589}{6170538644}e^{9} - \frac{17712352789869}{49364309152}e^{7} - \frac{14243936079161}{24682154576}e^{5} - \frac{389031902189}{3085269322}e^{3} + \frac{10801580202}{1542634661}e$
47 $[47, 47, w + 14]$ $-\frac{14393896651}{197457236608}e^{15} - \frac{214634309891}{49364309152}e^{13} - \frac{9535175561123}{98728618304}e^{11} - \frac{24418403404905}{24682154576}e^{9} - \frac{908686079737995}{197457236608}e^{7} - \frac{387464679928047}{49364309152}e^{5} - \frac{32891696948741}{12341077288}e^{3} - \frac{164339698904}{1542634661}e$
47 $[47, 47, w + 33]$ $\phantom{-}\frac{14327183695}{197457236608}e^{15} + \frac{106749886195}{24682154576}e^{13} + \frac{9474305202215}{98728618304}e^{11} + \frac{1513285416205}{1542634661}e^{9} + \frac{896875588432655}{197457236608}e^{7} + \frac{188418086654301}{24682154576}e^{5} + \frac{29016858604309}{12341077288}e^{3} + \frac{27540971699}{1542634661}e$
49 $[49, 7, -7]$ $-\frac{3379136249}{98728618304}e^{14} - \frac{50369926127}{24682154576}e^{12} - \frac{2236317229233}{49364309152}e^{10} - \frac{5720179933851}{12341077288}e^{8} - \frac{212287321917097}{98728618304}e^{6} - \frac{89710309134455}{24682154576}e^{4} - \frac{1790169374014}{1542634661}e^{2} - \frac{33844657779}{1542634661}$
67 $[67, 67, w + 16]$ $\phantom{-}\frac{2252603969}{197457236608}e^{15} + \frac{16784664869}{24682154576}e^{13} + \frac{1489807213169}{98728618304}e^{11} + \frac{1903971504037}{12341077288}e^{9} + \frac{141090951049745}{197457236608}e^{7} + \frac{29650160812085}{24682154576}e^{5} + \frac{4543051356795}{12341077288}e^{3} + \frac{4978133793}{1542634661}e$
67 $[67, 67, w + 51]$ $\phantom{-}\frac{4881627333}{197457236608}e^{15} + \frac{18220344015}{12341077288}e^{13} + \frac{3244443943861}{98728618304}e^{11} + \frac{521271089224}{1542634661}e^{9} + \frac{312975583928149}{197457236608}e^{7} + \frac{34219369370425}{12341077288}e^{5} + \frac{13346681658047}{12341077288}e^{3} + \frac{131912604271}{1542634661}e$
73 $[73, 73, w + 36]$ $\phantom{-}\frac{43753465191}{987286183040}e^{15} + \frac{162892191409}{61705386440}e^{13} + \frac{28881581421911}{493643091520}e^{11} + \frac{18413484949579}{30852693220}e^{9} + \frac{2715226106889463}{987286183040}e^{7} + \frac{280742250768981}{61705386440}e^{5} + \frac{76428593580063}{61705386440}e^{3} - \frac{445633937523}{7713173305}e$
73 $[73, 73, w + 37]$ $-\frac{18549205529}{246821545760}e^{15} - \frac{34569471773}{7713173305}e^{13} - \frac{12282966685829}{123410772880}e^{11} - \frac{31440029252809}{30852693220}e^{9} - \frac{1168676076489697}{246821545760}e^{7} - \frac{248228937148913}{30852693220}e^{5} - \frac{41041406739677}{15426346610}e^{3} - \frac{587067966252}{7713173305}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $\frac{11523}{1313824}e^{15} + \frac{686685}{1313824}e^{13} + \frac{951877}{82114}e^{11} + \frac{9723097}{82114}e^{9} + \frac{719100509}{1313824}e^{7} + \frac{1202061251}{1313824}e^{5} + \frac{11145560}{41057}e^{3} - \frac{59629}{41057}e$