Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3,3,-w + 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 6x^{11} + 28x^{10} - 66x^{9} + 136x^{8} - 146x^{7} + 227x^{6} - 172x^{5} + 286x^{4} - 90x^{3} + 130x^{2} - 14x + 49\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 9]$ | $...$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 5 | $[5, 5, w + 2]$ | $...$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $...$ |
| 7 | $[7, 7, w + 4]$ | $...$ |
| 13 | $[13, 13, w + 1]$ | $...$ |
| 13 | $[13, 13, w + 12]$ | $...$ |
| 43 | $[43, 43, -w - 6]$ | $...$ |
| 43 | $[43, 43, w - 6]$ | $...$ |
| 47 | $[47, 47, w + 19]$ | $...$ |
| 47 | $[47, 47, w + 28]$ | $...$ |
| 59 | $[59, 59, w + 16]$ | $...$ |
| 59 | $[59, 59, w + 43]$ | $...$ |
| 71 | $[71, 71, w + 24]$ | $...$ |
| 71 | $[71, 71, w + 47]$ | $...$ |
| 73 | $[73, 73, 3w - 28]$ | $...$ |
| 73 | $[73, 73, 12w - 107]$ | $...$ |
| 79 | $[79, 79, -w]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 1]$ | $-\frac{2046124}{1210169653}e^{11} - \frac{754515}{2420339306}e^{10} + \frac{2717735}{172881379}e^{9} - \frac{433690505}{2420339306}e^{8} + \frac{535755260}{1210169653}e^{7} - \frac{2602589485}{2420339306}e^{6} + \frac{2148877699}{2420339306}e^{5} - \frac{1943011065}{1210169653}e^{4} + \frac{2253675115}{2420339306}e^{3} - \frac{578285839}{220030846}e^{2} + \frac{810473885}{2420339306}e - \frac{90553465}{345762758}$ |