Base field 4.4.18432.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 18\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4x^{3} - 28x^{2} - 64x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{13}{5}e - \frac{14}{5}$ |
7 | $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ | $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{18}{5}e - \frac{14}{5}$ |
7 | $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ | $-\frac{1}{10}e^{3} - \frac{3}{10}e^{2} + \frac{18}{5}e + \frac{24}{5}$ |
7 | $[7, 7, \frac{1}{3}w^{2} + w - 1]$ | $-\frac{1}{10}e^{3} - \frac{3}{10}e^{2} + \frac{18}{5}e + \frac{24}{5}$ |
7 | $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{18}{5}e - \frac{14}{5}$ |
9 | $[9, 3, w - 3]$ | $-\frac{1}{5}e^{3} - \frac{3}{5}e^{2} + \frac{26}{5}e + \frac{28}{5}$ |
41 | $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $-\frac{1}{10}e^{3} + \frac{1}{5}e^{2} + \frac{18}{5}e - \frac{26}{5}$ |
41 | $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ | $-\frac{1}{10}e^{3} - \frac{4}{5}e^{2} + \frac{8}{5}e + \frac{54}{5}$ |
41 | $[41, 41, \frac{1}{3}w^{2} + w - 3]$ | $-\frac{1}{10}e^{3} - \frac{4}{5}e^{2} + \frac{8}{5}e + \frac{54}{5}$ |
41 | $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ | $-\frac{1}{10}e^{3} + \frac{1}{5}e^{2} + \frac{18}{5}e - \frac{26}{5}$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ | $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$ |
47 | $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ | $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$ |
47 | $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$ |
89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ | $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$ |
89 | $[89, 89, \frac{2}{3}w^{2} + w - 5]$ | $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$ |
89 | $[89, 89, \frac{2}{3}w^{2} - w - 5]$ | $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$ |
89 | $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ | $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$ |
97 | $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ | $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{36}{5}e - \frac{48}{5}$ |
97 | $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ | $-\frac{1}{5}e^{3} - \frac{3}{5}e^{2} + \frac{36}{5}e + \frac{28}{5}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).