Base field 4.4.5725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 5x^{5} - 11x^{4} - 111x^{3} - 248x^{2} - 225x - 72\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w + 1]$ | $\phantom{-}e^{5} + 3e^{4} - 17e^{3} - 77e^{2} - 94e - 38$ |
| 11 | $[11, 11, w]$ | $\phantom{-}\frac{5}{3}e^{5} + \frac{19}{3}e^{4} - \frac{79}{3}e^{3} - 154e^{2} - \frac{661}{3}e - 92$ |
| 11 | $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ | $-\frac{5}{3}e^{5} - \frac{16}{3}e^{4} + \frac{85}{3}e^{3} + 135e^{2} + \frac{487}{3}e + 53$ |
| 11 | $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ | $-\frac{11}{3}e^{5} - \frac{40}{3}e^{4} + \frac{175}{3}e^{3} + 327e^{2} + \frac{1402}{3}e + 201$ |
| 11 | $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ | $\phantom{-}\frac{10}{3}e^{5} + \frac{35}{3}e^{4} - \frac{161}{3}e^{3} - 289e^{2} - \frac{1208}{3}e - 168$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{5} + 3e^{4} - 17e^{3} - 77e^{2} - 93e - 36$ |
| 25 | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - \frac{20}{3}e^{3} - 20e^{2} - \frac{14}{3}e + 9$ |
| 29 | $[29, 29, -w - 3]$ | $-4e^{5} - 15e^{4} + 63e^{3} + 365e^{2} + 531e + 232$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ | $-\frac{17}{3}e^{5} - \frac{58}{3}e^{4} + \frac{277}{3}e^{3} + 482e^{2} + \frac{1957}{3}e + 261$ |
| 31 | $[31, 31, w^{3} - 6w + 1]$ | $\phantom{-}e^{5} + 4e^{4} - 15e^{3} - 96e^{2} - 153e - 74$ |
| 31 | $[31, 31, w^{3} - 6w - 2]$ | $\phantom{-}\frac{11}{3}e^{5} + \frac{43}{3}e^{4} - \frac{172}{3}e^{3} - 345e^{2} - \frac{1528}{3}e - 228$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ | $\phantom{-}\frac{8}{3}e^{5} + \frac{31}{3}e^{4} - \frac{124}{3}e^{3} - 250e^{2} - \frac{1123}{3}e - 163$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ | $\phantom{-}e^{5} + 3e^{4} - 17e^{3} - 78e^{2} - 94e - 25$ |
| 59 | $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ | $-5e^{5} - 19e^{4} + 77e^{3} + 462e^{2} + 698e + 317$ |
| 59 | $[59, 59, w^{3} + w^{2} - 6w - 4]$ | $\phantom{-}2e^{5} + 8e^{4} - 30e^{3} - 192e^{2} - 306e - 146$ |
| 79 | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $\phantom{-}1$ |
| 79 | $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ | $\phantom{-}\frac{20}{3}e^{5} + \frac{73}{3}e^{4} - \frac{325}{3}e^{3} - 596e^{2} - \frac{2428}{3}e - 311$ |
| 89 | $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ | $\phantom{-}4e^{5} + 15e^{4} - 65e^{3} - 364e^{2} - 496e - 194$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ | $-8e^{5} - 28e^{4} + 130e^{3} + 692e^{2} + 946e + 392$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $79$ | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $-1$ |