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: | $[59,59,\frac{1}{3}w^{3} - \frac{2}{3}w + \frac{7}{3}]$ |
Dimension: | $13$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{13} - 13x^{12} + 12x^{11} + 474x^{10} - 1879x^{9} - 1896x^{8} + 18824x^{7} - 13900x^{6} - 42512x^{5} + 37936x^{4} + 44992x^{3} - 23680x^{2} - 23040x - 2304\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ | $...$ |
9 | $[9, 3, -w + 1]$ | $\phantom{-}e$ |
11 | $[11, 11, w]$ | $...$ |
11 | $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ | $...$ |
11 | $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ | $...$ |
11 | $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ | $...$ |
16 | $[16, 2, 2]$ | $...$ |
25 | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ | $...$ |
29 | $[29, 29, -w - 3]$ | $...$ |
29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ | $...$ |
31 | $[31, 31, w^{3} - 6w + 1]$ | $...$ |
31 | $[31, 31, w^{3} - 6w - 2]$ | $...$ |
41 | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ | $...$ |
41 | $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ | $...$ |
59 | $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ | $...$ |
59 | $[59, 59, w^{3} + w^{2} - 6w - 4]$ | $-1$ |
79 | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $...$ |
79 | $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ | $...$ |
89 | $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ | $...$ |
89 | $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$59$ | $[59,59,\frac{1}{3}w^{3} - \frac{2}{3}w + \frac{7}{3}]$ | $1$ |