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: | $[3, 3, -2w - 21]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $126$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 15x^{10} + 77x^{8} - 166x^{6} + 158x^{4} - 65x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-\frac{34}{15}e^{11} + \frac{161}{5}e^{9} - \frac{2234}{15}e^{7} + \frac{3862}{15}e^{5} - \frac{2261}{15}e^{3} + \frac{332}{15}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w - 21]$ | $\phantom{-}1$ |
| 3 | $[3, 3, 2w - 23]$ | $-\frac{13}{5}e^{10} + \frac{186}{5}e^{8} - \frac{873}{5}e^{6} + \frac{1564}{5}e^{4} - \frac{1012}{5}e^{2} + \frac{189}{5}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{31}{15}e^{11} - \frac{149}{5}e^{9} + \frac{2126}{15}e^{7} - \frac{3898}{15}e^{5} + \frac{2609}{15}e^{3} - \frac{503}{15}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}\frac{34}{15}e^{11} - \frac{161}{5}e^{9} + \frac{2234}{15}e^{7} - \frac{3862}{15}e^{5} + \frac{2261}{15}e^{3} - \frac{332}{15}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{43}{15}e^{11} + \frac{207}{5}e^{9} - \frac{2963}{15}e^{7} + \frac{5464}{15}e^{5} - \frac{3662}{15}e^{3} + \frac{659}{15}e$ |
| 19 | $[19, 19, w + 2]$ | $-3e^{11} + 43e^{9} - 202e^{7} + 359e^{5} - 218e^{3} + 29e$ |
| 19 | $[19, 19, w + 16]$ | $-\frac{2}{3}e^{11} + 10e^{9} - \frac{154}{3}e^{7} + \frac{332}{3}e^{5} - \frac{313}{3}e^{3} + \frac{103}{3}e$ |
| 31 | $[31, 31, w + 13]$ | $-\frac{13}{5}e^{11} + \frac{186}{5}e^{9} - \frac{873}{5}e^{7} + \frac{1564}{5}e^{5} - \frac{1017}{5}e^{3} + \frac{199}{5}e$ |
| 31 | $[31, 31, w + 17]$ | $\phantom{-}\frac{68}{15}e^{11} - \frac{327}{5}e^{9} + \frac{4678}{15}e^{7} - \frac{8654}{15}e^{5} + \frac{5932}{15}e^{3} - \frac{1204}{15}e$ |
| 37 | $[37, 37, w + 18]$ | $\phantom{-}\frac{112}{15}e^{11} - \frac{538}{5}e^{9} + \frac{7682}{15}e^{7} - \frac{14176}{15}e^{5} + \frac{9758}{15}e^{3} - \frac{2081}{15}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{19}{5}e^{10} - \frac{268}{5}e^{8} + \frac{1224}{5}e^{6} - \frac{2067}{5}e^{4} + \frac{1176}{5}e^{2} - \frac{197}{5}$ |
| 53 | $[53, 53, -234w + 2683]$ | $\phantom{-}\frac{58}{5}e^{10} - \frac{826}{5}e^{8} + \frac{3843}{5}e^{6} - \frac{6759}{5}e^{4} + \frac{4197}{5}e^{2} - \frac{734}{5}$ |
| 53 | $[53, 53, -234w - 2449]$ | $-\frac{22}{5}e^{10} + \frac{319}{5}e^{8} - \frac{1532}{5}e^{6} + \frac{2856}{5}e^{4} - \frac{1948}{5}e^{2} + \frac{361}{5}$ |
| 59 | $[59, 59, w + 1]$ | $-\frac{26}{3}e^{11} + 125e^{9} - \frac{1786}{3}e^{7} + \frac{3290}{3}e^{5} - \frac{2233}{3}e^{3} + \frac{466}{3}e$ |
| 59 | $[59, 59, w + 57]$ | $-\frac{76}{15}e^{11} + \frac{364}{5}e^{9} - \frac{5171}{15}e^{7} + \frac{9463}{15}e^{5} - \frac{6479}{15}e^{3} + \frac{1478}{15}e$ |
| 89 | $[89, 89, w + 41]$ | $\phantom{-}\frac{79}{15}e^{11} - \frac{381}{5}e^{9} + \frac{5489}{15}e^{7} - \frac{10372}{15}e^{5} + \frac{7646}{15}e^{3} - \frac{1832}{15}e$ |
| 89 | $[89, 89, w + 47]$ | $\phantom{-}\frac{13}{5}e^{11} - \frac{181}{5}e^{9} + \frac{803}{5}e^{7} - \frac{1254}{5}e^{5} + \frac{542}{5}e^{3} - \frac{19}{5}e$ |
| 97 | $[97, 97, w + 26]$ | $\phantom{-}\frac{73}{5}e^{11} - \frac{1036}{5}e^{9} + \frac{4783}{5}e^{7} - \frac{8239}{5}e^{5} + \frac{4787}{5}e^{3} - \frac{664}{5}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -2w - 21]$ | $-1$ |