Base field \(\Q(\sqrt{145}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 36\); narrow class number \(4\) and class number \(4\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} + 2x^{2} - 2x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{1}{2}e + \frac{1}{2}$ |
| 3 | $[3, 3, w]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{3}{2}e + \frac{3}{2}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{3}{2}e + \frac{1}{2}$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 1]$ | $-\frac{3}{2}e^{3} - \frac{9}{2}e^{2} - \frac{13}{2}e - \frac{3}{2}$ |
| 17 | $[17, 17, w + 15]$ | $\phantom{-}\frac{5}{2}e^{3} + \frac{11}{2}e^{2} + \frac{11}{2}e - \frac{11}{2}$ |
| 29 | $[29, 29, w + 14]$ | $\phantom{-}0$ |
| 37 | $[37, 37, w + 10]$ | $\phantom{-}\frac{9}{2}e^{3} + \frac{15}{2}e^{2} + \frac{15}{2}e - \frac{15}{2}$ |
| 37 | $[37, 37, w + 26]$ | $-\frac{3}{2}e^{3} - \frac{9}{2}e^{2} - \frac{21}{2}e - \frac{3}{2}$ |
| 43 | $[43, 43, w + 19]$ | $-\frac{3}{2}e^{3} - \frac{9}{2}e^{2} - \frac{9}{2}e + \frac{9}{2}$ |
| 43 | $[43, 43, w + 23]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{9}{2}e^{2} + \frac{9}{2}e + \frac{3}{2}$ |
| 47 | $[47, 47, w + 22]$ | $-\frac{3}{2}e^{3} - \frac{9}{2}e^{2} - \frac{17}{2}e - \frac{3}{2}$ |
| 47 | $[47, 47, w + 24]$ | $\phantom{-}\frac{7}{2}e^{3} + \frac{13}{2}e^{2} + \frac{13}{2}e - \frac{13}{2}$ |
| 49 | $[49, 7, -7]$ | $-2e^{3} - 2e^{2} + 2e + 8$ |
| 59 | $[59, 59, w + 16]$ | $-6e^{3} - 12e^{2} - 18e + 6$ |
| 59 | $[59, 59, w + 42]$ | $\phantom{-}6e^{3} + 12e^{2} + 18e - 6$ |
| 71 | $[71, 71, w + 21]$ | $-6e^{3} - 12e^{2} - 18e + 6$ |
| 71 | $[71, 71, w + 49]$ | $\phantom{-}6e^{3} + 12e^{2} + 18e - 6$ |
| 73 | $[73, 73, w + 13]$ | $-\frac{9}{2}e^{3} - \frac{27}{2}e^{2} - \frac{39}{2}e - \frac{9}{2}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).