Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[16, 4, 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $108$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 16x^{6} + 73x^{4} - 82x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -w + 8]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{13}{8}e^{4} + \frac{21}{4}e^{2} - \frac{7}{2}$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{3}{16}e^{7} + \frac{47}{16}e^{5} - \frac{99}{8}e^{3} + \frac{37}{4}e$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{3}{16}e^{7} + \frac{47}{16}e^{5} - \frac{99}{8}e^{3} + \frac{37}{4}e$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{21}{16}e^{5} + \frac{65}{8}e^{3} - \frac{51}{4}e$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{21}{16}e^{5} + \frac{65}{8}e^{3} - \frac{51}{4}e$ |
| 17 | $[17, 17, w]$ | $\phantom{-}\frac{3}{8}e^{7} - \frac{47}{8}e^{5} + \frac{103}{4}e^{3} - \frac{53}{2}e$ |
| 17 | $[17, 17, w + 16]$ | $\phantom{-}\frac{3}{8}e^{7} - \frac{47}{8}e^{5} + \frac{103}{4}e^{3} - \frac{53}{2}e$ |
| 31 | $[31, 31, -w - 4]$ | $-\frac{3}{16}e^{6} + \frac{31}{16}e^{4} - \frac{27}{8}e^{2} - \frac{7}{4}$ |
| 31 | $[31, 31, w - 5]$ | $-\frac{3}{16}e^{6} + \frac{31}{16}e^{4} - \frac{27}{8}e^{2} - \frac{7}{4}$ |
| 41 | $[41, 41, 3w - 22]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{21}{8}e^{4} + \frac{57}{4}e^{2} - \frac{15}{2}$ |
| 47 | $[47, 47, w + 19]$ | $\phantom{-}\frac{9}{16}e^{7} - \frac{141}{16}e^{5} + \frac{321}{8}e^{3} - \frac{199}{4}e$ |
| 47 | $[47, 47, w + 27]$ | $\phantom{-}\frac{9}{16}e^{7} - \frac{141}{16}e^{5} + \frac{321}{8}e^{3} - \frac{199}{4}e$ |
| 53 | $[53, 53, w + 14]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{13}{8}e^{5} + \frac{21}{4}e^{3} - \frac{3}{2}e$ |
| 53 | $[53, 53, w + 38]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{13}{8}e^{5} + \frac{21}{4}e^{3} - \frac{3}{2}e$ |
| 59 | $[59, 59, -w - 10]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{37}{16}e^{4} + \frac{121}{8}e^{2} - \frac{35}{4}$ |
| 59 | $[59, 59, w - 11]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{37}{16}e^{4} + \frac{121}{8}e^{2} - \frac{35}{4}$ |
| 61 | $[61, 61, 2w - 13]$ | $-\frac{3}{8}e^{6} + \frac{39}{8}e^{4} - \frac{59}{4}e^{2} + \frac{5}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |