Base field 4.4.4525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 3x + 9\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[31,31,\frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 4x^{3} - 5x^{2} + 25x - 18\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ | $\phantom{-}3e^{3} - 8e^{2} - 26e + 42$ |
5 | $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ | $\phantom{-}e$ |
9 | $[9, 3, -w]$ | $\phantom{-}2e^{3} - 5e^{2} - 18e + 26$ |
9 | $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ | $\phantom{-}2e^{3} - 5e^{2} - 18e + 26$ |
16 | $[16, 2, 2]$ | $-e - 1$ |
19 | $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ | $-2e^{3} + 5e^{2} + 19e - 26$ |
19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ | $\phantom{-}e^{3} - 2e^{2} - 9e + 10$ |
31 | $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ | $-3e^{3} + 7e^{2} + 26e - 32$ |
31 | $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ | $-1$ |
41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ | $\phantom{-}6e^{3} - 15e^{2} - 52e + 78$ |
41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ | $-7e^{3} + 19e^{2} + 61e - 96$ |
61 | $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ | $\phantom{-}e^{3} - 2e^{2} - 10e + 10$ |
61 | $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ | $-6e^{3} + 16e^{2} + 49e - 80$ |
71 | $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ | $-e^{3} + 3e^{2} + 8e - 12$ |
71 | $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ | $-e^{3} + e^{2} + 10e$ |
89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ | $\phantom{-}2e^{3} - 6e^{2} - 18e + 30$ |
89 | $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $\phantom{-}12e^{3} - 33e^{2} - 103e + 168$ |
101 | $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ | $-12e^{3} + 33e^{2} + 102e - 162$ |
101 | $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ | $-4e^{3} + 10e^{2} + 37e - 48$ |
101 | $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ | $\phantom{-}13e^{3} - 35e^{2} - 110e + 174$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31,31,\frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ | $1$ |