Base field \(\Q(\sqrt{481}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 120\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} - 27x^{18} + 303x^{16} - 1840x^{14} + 6599x^{12} - 14301x^{10} + 18338x^{8} - 12960x^{6} + 4353x^{4} - 546x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w - 21]$ | $-\frac{104}{1901}e^{18} + \frac{2480}{1901}e^{16} - \frac{23398}{1901}e^{14} + \frac{110401}{1901}e^{12} - \frac{267625}{1901}e^{10} + \frac{287184}{1901}e^{8} - \frac{23134}{1901}e^{6} - \frac{134347}{1901}e^{4} + \frac{20704}{1901}e^{2} + \frac{4073}{1901}$ |
| 3 | $[3, 3, 2w - 23]$ | $-\frac{104}{1901}e^{18} + \frac{2480}{1901}e^{16} - \frac{23398}{1901}e^{14} + \frac{110401}{1901}e^{12} - \frac{267625}{1901}e^{10} + \frac{287184}{1901}e^{8} - \frac{23134}{1901}e^{6} - \frac{134347}{1901}e^{4} + \frac{20704}{1901}e^{2} + \frac{4073}{1901}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{239}{1901}e^{19} - \frac{13007}{3802}e^{17} + \frac{73475}{1901}e^{15} - \frac{895553}{3802}e^{13} + \frac{3201273}{3802}e^{11} - \frac{3412034}{1901}e^{9} + \frac{8398855}{3802}e^{7} - \frac{5434025}{3802}e^{5} + \frac{1509139}{3802}e^{3} - \frac{68090}{1901}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}\frac{239}{1901}e^{19} - \frac{13007}{3802}e^{17} + \frac{73475}{1901}e^{15} - \frac{895553}{3802}e^{13} + \frac{3201273}{3802}e^{11} - \frac{3412034}{1901}e^{9} + \frac{8398855}{3802}e^{7} - \frac{5434025}{3802}e^{5} + \frac{1509139}{3802}e^{3} - \frac{68090}{1901}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{224}{1901}e^{19} + \frac{5634}{1901}e^{17} - \frac{57561}{1901}e^{15} + \frac{308270}{1901}e^{13} - \frac{932495}{1901}e^{11} + \frac{1594933}{1901}e^{9} - \frac{1434340}{1901}e^{7} + \frac{505109}{1901}e^{5} + \frac{78665}{1901}e^{3} - \frac{60687}{1901}e$ |
| 19 | $[19, 19, w + 2]$ | $-\frac{272}{1901}e^{19} + \frac{7656}{1901}e^{17} - \frac{89856}{1901}e^{15} + \frac{570674}{1901}e^{13} - \frac{2126131}{1901}e^{11} + \frac{4692747}{1901}e^{9} - \frac{5847587}{1901}e^{7} + \frac{3571710}{1901}e^{5} - \frac{699232}{1901}e^{3} - \frac{2947}{1901}e$ |
| 19 | $[19, 19, w + 16]$ | $-\frac{272}{1901}e^{19} + \frac{7656}{1901}e^{17} - \frac{89856}{1901}e^{15} + \frac{570674}{1901}e^{13} - \frac{2126131}{1901}e^{11} + \frac{4692747}{1901}e^{9} - \frac{5847587}{1901}e^{7} + \frac{3571710}{1901}e^{5} - \frac{699232}{1901}e^{3} - \frac{2947}{1901}e$ |
| 31 | $[31, 31, w + 13]$ | $-\frac{449}{3802}e^{19} + \frac{12023}{3802}e^{17} - \frac{132785}{3802}e^{15} + \frac{391083}{1901}e^{13} - \frac{2646297}{3802}e^{11} + \frac{5109859}{3802}e^{9} - \frac{2547505}{1901}e^{7} + \frac{851094}{1901}e^{5} + \frac{593443}{3802}e^{3} - \frac{115769}{1901}e$ |
| 31 | $[31, 31, w + 17]$ | $-\frac{449}{3802}e^{19} + \frac{12023}{3802}e^{17} - \frac{132785}{3802}e^{15} + \frac{391083}{1901}e^{13} - \frac{2646297}{3802}e^{11} + \frac{5109859}{3802}e^{9} - \frac{2547505}{1901}e^{7} + \frac{851094}{1901}e^{5} + \frac{593443}{3802}e^{3} - \frac{115769}{1901}e$ |
| 37 | $[37, 37, w + 18]$ | $-\frac{337}{1901}e^{19} + \frac{9206}{1901}e^{17} - \frac{104955}{1901}e^{15} + \frac{650843}{1901}e^{13} - \frac{2397714}{1901}e^{11} + \frac{5366497}{1901}e^{9} - \frac{7120983}{1901}e^{7} + \frac{5170841}{1901}e^{5} - \frac{1735644}{1901}e^{3} + \frac{198966}{1901}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{831}{3802}e^{18} - \frac{10493}{1901}e^{16} + \frac{215145}{3802}e^{14} - \frac{1152911}{3802}e^{12} + \frac{1732050}{1901}e^{10} - \frac{5799131}{3802}e^{8} + \frac{5013353}{3802}e^{6} - \frac{1843253}{3802}e^{4} + \frac{81062}{1901}e^{2} + \frac{21775}{1901}$ |
| 53 | $[53, 53, -234w + 2683]$ | $-\frac{219}{3802}e^{18} + \frac{1880}{1901}e^{16} - \frac{12969}{3802}e^{14} - \frac{130155}{3802}e^{12} + \frac{652481}{1901}e^{10} - \frac{4680183}{3802}e^{8} + \frac{7969301}{3802}e^{6} - \frac{6060975}{3802}e^{4} + \frac{707475}{1901}e^{2} - \frac{16321}{1901}$ |
| 53 | $[53, 53, -234w - 2449]$ | $-\frac{219}{3802}e^{18} + \frac{1880}{1901}e^{16} - \frac{12969}{3802}e^{14} - \frac{130155}{3802}e^{12} + \frac{652481}{1901}e^{10} - \frac{4680183}{3802}e^{8} + \frac{7969301}{3802}e^{6} - \frac{6060975}{3802}e^{4} + \frac{707475}{1901}e^{2} - \frac{16321}{1901}$ |
| 59 | $[59, 59, w + 1]$ | $-\frac{1417}{1901}e^{19} + \frac{37592}{1901}e^{17} - \frac{412422}{1901}e^{15} + \frac{2431664}{1901}e^{13} - \frac{8385346}{1901}e^{11} + \frac{17208476}{1901}e^{9} - \frac{20321800}{1901}e^{7} + \frac{12439141}{1901}e^{5} - \frac{3071272}{1901}e^{3} + \frac{213040}{1901}e$ |
| 59 | $[59, 59, w + 57]$ | $-\frac{1417}{1901}e^{19} + \frac{37592}{1901}e^{17} - \frac{412422}{1901}e^{15} + \frac{2431664}{1901}e^{13} - \frac{8385346}{1901}e^{11} + \frac{17208476}{1901}e^{9} - \frac{20321800}{1901}e^{7} + \frac{12439141}{1901}e^{5} - \frac{3071272}{1901}e^{3} + \frac{213040}{1901}e$ |
| 89 | $[89, 89, w + 41]$ | $-\frac{113}{3802}e^{19} + \frac{1671}{3802}e^{17} + \frac{131}{3802}e^{15} - \frac{69190}{1901}e^{13} + \frac{1070715}{3802}e^{11} - \frac{3701267}{3802}e^{9} + \frac{3276948}{1901}e^{7} - \frac{2853062}{1901}e^{5} + \frac{2002899}{3802}e^{3} - \frac{84036}{1901}e$ |
| 89 | $[89, 89, w + 47]$ | $-\frac{113}{3802}e^{19} + \frac{1671}{3802}e^{17} + \frac{131}{3802}e^{15} - \frac{69190}{1901}e^{13} + \frac{1070715}{3802}e^{11} - \frac{3701267}{3802}e^{9} + \frac{3276948}{1901}e^{7} - \frac{2853062}{1901}e^{5} + \frac{2002899}{3802}e^{3} - \frac{84036}{1901}e$ |
| 97 | $[97, 97, w + 26]$ | $-\frac{653}{3802}e^{19} + \frac{7932}{1901}e^{17} - \frac{154553}{3802}e^{15} + \frac{775793}{3802}e^{13} - \frac{1080363}{1901}e^{11} + \frac{3433511}{3802}e^{9} - \frac{3397025}{3802}e^{7} + \frac{2769873}{3802}e^{5} - \frac{932149}{1901}e^{3} + \frac{237900}{1901}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).