Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 2, 2]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{134}{2055}e^{7} - \frac{232}{2055}e^{6} + \frac{979}{2055}e^{5} - \frac{97}{2055}e^{4} + \frac{3424}{2055}e^{3} - \frac{1471}{2055}e^{2} + \frac{5759}{2055}e + \frac{787}{685}$ |
4 | $[4, 2, 2]$ | $\phantom{-}1$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1327}{6165}e^{7} - \frac{2686}{6165}e^{6} + \frac{10927}{6165}e^{5} - \frac{2806}{6165}e^{4} + \frac{30217}{6165}e^{3} - \frac{5923}{6165}e^{2} + \frac{16129}{2055}e + \frac{2177}{685}$ |
5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{263}{6165}e^{7} - \frac{1079}{6165}e^{6} + \frac{3818}{6165}e^{5} - \frac{4694}{6165}e^{4} + \frac{10043}{6165}e^{3} - \frac{9047}{6165}e^{2} + \frac{9931}{2055}e - \frac{332}{685}$ |
11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{794}{6165}e^{7} - \frac{1937}{6165}e^{6} + \frac{6854}{6165}e^{5} - \frac{4787}{6165}e^{4} + \frac{18029}{6165}e^{3} - \frac{16241}{6165}e^{2} + \frac{11828}{2055}e - \frac{596}{685}$ |
11 | $[11, 11, w + 9]$ | $-\frac{98}{6165}e^{7} + \frac{824}{6165}e^{6} - \frac{1493}{6165}e^{5} + \frac{3179}{6165}e^{4} + \frac{3712}{6165}e^{3} + \frac{5012}{6165}e^{2} + \frac{3449}{2055}e + \frac{517}{685}$ |
17 | $[17, 17, w + 2]$ | $\phantom{-}\frac{857}{6165}e^{7} - \frac{1586}{6165}e^{6} + \frac{5612}{6165}e^{5} - \frac{1106}{6165}e^{4} + \frac{14762}{6165}e^{3} - \frac{13298}{6165}e^{2} + \frac{3299}{2055}e - \frac{488}{685}$ |
17 | $[17, 17, w + 14]$ | $-\frac{2153}{6165}e^{7} + \frac{4934}{6165}e^{6} - \frac{17933}{6165}e^{5} + \frac{7289}{6165}e^{4} - \frac{43553}{6165}e^{3} + \frac{21452}{6165}e^{2} - \frac{21896}{2055}e - \frac{2908}{685}$ |
19 | $[19, 19, w]$ | $\phantom{-}\frac{401}{6165}e^{7} - \frac{1778}{6165}e^{6} + \frac{3446}{6165}e^{5} - \frac{5438}{6165}e^{4} - \frac{49}{6165}e^{3} - \frac{23444}{6165}e^{2} - \frac{2293}{2055}e - \frac{389}{685}$ |
19 | $[19, 19, w + 18]$ | $-\frac{2177}{6165}e^{7} + \frac{5681}{6165}e^{6} - \frac{20102}{6165}e^{5} + \frac{15281}{6165}e^{4} - \frac{52877}{6165}e^{3} + \frac{47633}{6165}e^{2} - \frac{10293}{685}e + \frac{1748}{685}$ |
37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{148}{2055}e^{7} - \frac{154}{2055}e^{6} + \frac{703}{2055}e^{5} + \frac{1406}{2055}e^{4} + \frac{643}{2055}e^{3} + \frac{3293}{2055}e^{2} + \frac{481}{685}e + \frac{2914}{685}$ |
37 | $[37, 37, w - 5]$ | $-\frac{112}{2055}e^{7} + \frac{61}{2055}e^{6} - \frac{532}{2055}e^{5} - \frac{1064}{2055}e^{4} - \frac{1042}{2055}e^{3} - \frac{2492}{2055}e^{2} - \frac{364}{685}e + \frac{794}{685}$ |
43 | $[43, 43, w + 16]$ | $\phantom{-}\frac{16}{6165}e^{7} - \frac{1183}{6165}e^{6} + \frac{4186}{6165}e^{5} - \frac{10123}{6165}e^{4} + \frac{11011}{6165}e^{3} - \frac{9919}{6165}e^{2} + \frac{3899}{685}e - \frac{364}{685}$ |
43 | $[43, 43, w + 26]$ | $\phantom{-}\frac{2654}{6165}e^{7} - \frac{5372}{6165}e^{6} + \frac{21854}{6165}e^{5} - \frac{5612}{6165}e^{4} + \frac{60434}{6165}e^{3} - \frac{18011}{6165}e^{2} + \frac{32258}{2055}e + \frac{4354}{685}$ |
49 | $[49, 7, -7]$ | $-\frac{24}{685}e^{7} + \frac{62}{685}e^{6} - \frac{114}{685}e^{5} - \frac{228}{685}e^{4} + \frac{266}{685}e^{3} - \frac{534}{685}e^{2} - \frac{234}{685}e - \frac{6731}{685}$ |
53 | $[53, 53, -w - 10]$ | $\phantom{-}\frac{116}{2055}e^{7} + \frac{157}{2055}e^{6} + \frac{551}{2055}e^{5} + \frac{1102}{2055}e^{4} + \frac{5336}{2055}e^{3} + \frac{2581}{2055}e^{2} + \frac{377}{685}e - \frac{2437}{685}$ |
53 | $[53, 53, w - 11]$ | $-\frac{296}{2055}e^{7} + \frac{308}{2055}e^{6} - \frac{1406}{2055}e^{5} - \frac{2812}{2055}e^{4} - \frac{3341}{2055}e^{3} - \frac{6586}{2055}e^{2} - \frac{962}{685}e - \frac{8568}{685}$ |
61 | $[61, 61, w + 15]$ | $-\frac{2881}{6165}e^{7} + \frac{6358}{6165}e^{6} - \frac{23446}{6165}e^{5} + \frac{8593}{6165}e^{4} - \frac{60601}{6165}e^{3} + \frac{25804}{6165}e^{2} - \frac{31112}{2055}e - \frac{4156}{685}$ |
61 | $[61, 61, w + 45]$ | $\phantom{-}\frac{673}{6165}e^{7} - \frac{1339}{6165}e^{6} + \frac{4738}{6165}e^{5} - \frac{2854}{6165}e^{4} + \frac{12463}{6165}e^{3} - \frac{11227}{6165}e^{2} - \frac{3464}{2055}e - \frac{412}{685}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, 2]$ | $-1$ |