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: | $[2, 2, w]$ |
| Dimension: | $12$ |
| 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:
| \(x^{12} + 18x^{10} + 115x^{8} + 316x^{6} + 375x^{4} + 159x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{9}{41}e^{11} - \frac{156}{41}e^{9} - \frac{931}{41}e^{7} - \frac{2237}{41}e^{5} - \frac{2034}{41}e^{3} - \frac{526}{41}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w - 21]$ | $\phantom{-}\frac{25}{287}e^{10} + \frac{58}{41}e^{8} + \frac{2126}{287}e^{6} + \frac{3722}{287}e^{4} + \frac{976}{287}e^{2} - \frac{762}{287}$ |
| 3 | $[3, 3, 2w - 23]$ | $-\frac{48}{287}e^{10} - \frac{113}{41}e^{8} - \frac{4323}{287}e^{6} - \frac{8719}{287}e^{4} - \frac{5272}{287}e^{2} + \frac{51}{287}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{46}{287}e^{11} + \frac{110}{41}e^{9} + \frac{4394}{287}e^{7} + \frac{9994}{287}e^{5} + \frac{8879}{287}e^{3} + \frac{2570}{287}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}\frac{86}{287}e^{11} + \frac{211}{41}e^{9} + \frac{8714}{287}e^{7} + \frac{20656}{287}e^{5} + \frac{18534}{287}e^{3} + \frac{4106}{287}e$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}\frac{300}{287}e^{11} + \frac{737}{41}e^{9} + \frac{30391}{287}e^{7} + \frac{71068}{287}e^{5} + \frac{60215}{287}e^{3} + \frac{12381}{287}e$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}\frac{198}{287}e^{11} + \frac{502}{41}e^{9} + \frac{21958}{287}e^{7} + \frac{58316}{287}e^{5} + \frac{66519}{287}e^{3} + \frac{27521}{287}e$ |
| 19 | $[19, 19, w + 16]$ | $\phantom{-}\frac{179}{287}e^{11} + \frac{453}{41}e^{9} + \frac{19619}{287}e^{7} + \frac{50195}{287}e^{5} + \frac{50417}{287}e^{3} + \frac{14680}{287}e$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{284}{287}e^{11} + \frac{713}{41}e^{9} + \frac{30672}{287}e^{7} + \frac{78685}{287}e^{5} + \frac{82757}{287}e^{3} + \frac{29331}{287}e$ |
| 31 | $[31, 31, w + 17]$ | $-\frac{3}{7}e^{11} - 7e^{9} - \frac{261}{7}e^{7} - \frac{478}{7}e^{5} - \frac{151}{7}e^{3} + \frac{127}{7}e$ |
| 37 | $[37, 37, w + 18]$ | $-\frac{13}{41}e^{11} - \frac{198}{41}e^{9} - \frac{912}{41}e^{7} - \frac{958}{41}e^{5} + \frac{1490}{41}e^{3} + \frac{1887}{41}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{35}{41}e^{10} + \frac{593}{41}e^{8} + \frac{3411}{41}e^{6} + \frac{7556}{41}e^{4} + \frac{5286}{41}e^{2} + \frac{114}{41}$ |
| 53 | $[53, 53, -234w + 2683]$ | $\phantom{-}\frac{293}{287}e^{10} + \frac{706}{41}e^{8} + \frac{28200}{287}e^{6} + \frac{62185}{287}e^{4} + \frac{46005}{287}e^{2} + \frac{3043}{287}$ |
| 53 | $[53, 53, -234w - 2449]$ | $\phantom{-}\frac{75}{41}e^{10} + \frac{1259}{41}e^{8} + \frac{7116}{41}e^{6} + \frac{15307}{41}e^{4} + \frac{10554}{41}e^{2} + \frac{543}{41}$ |
| 59 | $[59, 59, w + 1]$ | $\phantom{-}\frac{128}{287}e^{11} + \frac{356}{41}e^{9} + \frac{17842}{287}e^{7} + \frac{57882}{287}e^{5} + \frac{85139}{287}e^{3} + \frac{46358}{287}e$ |
| 59 | $[59, 59, w + 57]$ | $\phantom{-}\frac{88}{287}e^{11} + \frac{214}{41}e^{9} + \frac{8643}{287}e^{7} + \frac{19668}{287}e^{5} + \frac{17797}{287}e^{3} + \frac{7512}{287}e$ |
| 89 | $[89, 89, w + 41]$ | $\phantom{-}\frac{176}{287}e^{11} + \frac{387}{41}e^{9} + \frac{12694}{287}e^{7} + \frac{14367}{287}e^{5} - \frac{17788}{287}e^{3} - \frac{23147}{287}e$ |
| 89 | $[89, 89, w + 47]$ | $\phantom{-}\frac{22}{287}e^{11} + \frac{74}{41}e^{9} + \frac{4385}{287}e^{7} + \frac{16397}{287}e^{5} + \frac{26333}{287}e^{3} + \frac{13071}{287}e$ |
| 97 | $[97, 97, w + 26]$ | $\phantom{-}\frac{18}{41}e^{11} + \frac{271}{41}e^{9} + \frac{1165}{41}e^{7} + \frac{497}{41}e^{5} - \frac{4460}{41}e^{3} - \frac{4565}{41}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $\frac{9}{41}e^{11} + \frac{156}{41}e^{9} + \frac{931}{41}e^{7} + \frac{2237}{41}e^{5} + \frac{2034}{41}e^{3} + \frac{526}{41}e$ |