Base field \(\Q(\sqrt{281}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 8x^{2} + 6x + 11\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w + 9]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e + \frac{1}{3}$ |
| 5 | $[5, 5, -76w + 675]$ | $\phantom{-}e + 1$ |
| 5 | $[5, 5, 76w + 599]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e + \frac{4}{3}$ |
| 7 | $[7, 7, -8w - 63]$ | $\phantom{-}\frac{1}{3}e^{3} + e^{2} - \frac{8}{3}e - \frac{8}{3}$ |
| 7 | $[7, 7, -8w + 71]$ | $-\frac{1}{3}e^{3} - e^{2} + \frac{8}{3}e + \frac{17}{3}$ |
| 9 | $[9, 3, 3]$ | $-\frac{2}{3}e^{3} + \frac{10}{3}e - \frac{5}{3}$ |
| 17 | $[17, 17, 42w + 331]$ | $-e^{3} + e^{2} + 6e - 4$ |
| 17 | $[17, 17, 42w - 373]$ | $-e^{3} - e^{2} + 4e + 5$ |
| 29 | $[29, 29, -6w - 47]$ | $\phantom{-}\frac{2}{3}e^{3} - e^{2} - \frac{10}{3}e + \frac{20}{3}$ |
| 29 | $[29, 29, 6w - 53]$ | $\phantom{-}e^{3} + e^{2} - 5e - 2$ |
| 31 | $[31, 31, 10w + 79]$ | $\phantom{-}\frac{4}{3}e^{3} + e^{2} - \frac{26}{3}e - \frac{14}{3}$ |
| 31 | $[31, 31, -10w + 89]$ | $\phantom{-}\frac{1}{3}e^{3} - e^{2} + \frac{1}{3}e + \frac{10}{3}$ |
| 43 | $[43, 43, 2w - 19]$ | $-e^{3} + 2e^{2} + 6e - 5$ |
| 43 | $[43, 43, -2w - 17]$ | $-\frac{4}{3}e^{3} - 2e^{2} + \frac{17}{3}e + \frac{38}{3}$ |
| 53 | $[53, 53, 194w + 1529]$ | $-e^{3} + 2e^{2} + 4e - 7$ |
| 53 | $[53, 53, -194w + 1723]$ | $-2e^{3} - 2e^{2} + 11e + 10$ |
| 59 | $[59, 59, -110w - 867]$ | $-\frac{1}{3}e^{3} + e^{2} + \frac{2}{3}e + \frac{14}{3}$ |
| 59 | $[59, 59, 110w - 977]$ | $-e^{3} - e^{2} + 6e + 13$ |
| 79 | $[79, 79, 650w - 5773]$ | $\phantom{-}\frac{2}{3}e^{3} + e^{2} + \frac{2}{3}e - \frac{19}{3}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).