Base field \(\Q(\sqrt{201}) \)
Generator \(w\), with minimal polynomial \(x^2 - x - 50\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6,6,-w + 8]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^6 - x^5 - 10 x^4 + 9 x^3 + 25 x^2 - 20 x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17 w - 112]$ | $-1$ |
| 2 | $[2, 2, -17 w + 129]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -124 w + 941]$ | $-1$ |
| 5 | $[5, 5, -2 w + 15]$ | $\phantom{-}\frac{1}{2} e^5 + \frac{1}{2} e^4 - 5 e^3 - \frac{7}{2} e^2 + \frac{21}{2} e + 3$ |
| 5 | $[5, 5, -2 w - 13]$ | $-e^2 + 3$ |
| 11 | $[11, 11, 12 w + 79]$ | $\phantom{-}\frac{1}{2} e^5 + \frac{1}{2} e^4 - 5 e^3 - \frac{7}{2} e^2 + \frac{25}{2} e + 3$ |
| 11 | $[11, 11, -12 w + 91]$ | $\phantom{-}e^3 - 5 e$ |
| 19 | $[19, 19, -90 w - 593]$ | $\phantom{-}e^5 - 8 e^3 - 2 e^2 + 13 e + 6$ |
| 19 | $[19, 19, 90 w - 683]$ | $-\frac{1}{2} e^5 - \frac{1}{2} e^4 + 5 e^3 + \frac{11}{2} e^2 - \frac{21}{2} e - 7$ |
| 37 | $[37, 37, -4 w - 27]$ | $\phantom{-}e^4 - e^3 - 7 e^2 + 5 e + 8$ |
| 37 | $[37, 37, -4 w + 31]$ | $-e^4 + 2 e^3 + 5 e^2 - 10 e$ |
| 41 | $[41, 41, 158 w + 1041]$ | $\phantom{-}\frac{1}{2} e^5 - \frac{1}{2} e^4 - 4 e^3 + \frac{7}{2} e^2 + \frac{11}{2} e - 3$ |
| 41 | $[41, 41, 158 w - 1199]$ | $\phantom{-}e^5 - 10 e^3 + 21 e - 6$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}e^4 - 2 e^3 - 7 e^2 + 10 e + 8$ |
| 53 | $[53, 53, 46 w - 349]$ | $-e^5 + 9 e^3 - 2 e^2 - 18 e + 8$ |
| 53 | $[53, 53, 46 w + 303]$ | $\phantom{-}e^5 - 9 e^3 - e^2 + 16 e + 3$ |
| 67 | $[67, 67, 586 w - 4447]$ | $\phantom{-}e^4 - 2 e^3 - 5 e^2 + 8 e + 2$ |
| 73 | $[73, 73, -32 w - 211]$ | $\phantom{-}e^5 - e^4 - 7 e^3 + 5 e^2 + 10 e - 2$ |
| 73 | $[73, 73, 32 w - 243]$ | $-e^5 + e^4 + 10 e^3 - 7 e^2 - 25 e + 8$ |
| 101 | $[101, 101, 2 w - 11]$ | $-2 e^5 - e^4 + 18 e^3 + 8 e^2 - 36 e - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,17 w + 112]$ | $1$ |
| $3$ | $[3,3,124 w + 817]$ | $1$ |