Base field 3.3.321.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[23, 23, -w - 3]$ |
Dimension: | $5$ |
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:
\(x^{5} - 3x^{4} - 9x^{3} + 26x^{2} + 10x - 37\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 1]$ | $-\frac{3}{4}e^{4} + e^{3} + \frac{31}{4}e^{2} - \frac{21}{4}e - \frac{49}{4}$ |
7 | $[7, 7, w^{2} - 2]$ | $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} + \frac{1}{4}e - \frac{23}{4}$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{7}{4}e^{4} - 2e^{3} - \frac{79}{4}e^{2} + \frac{41}{4}e + \frac{153}{4}$ |
11 | $[11, 11, -w^{2} + w + 1]$ | $\phantom{-}\frac{3}{2}e^{4} - 2e^{3} - \frac{33}{2}e^{2} + \frac{19}{2}e + \frac{63}{2}$ |
23 | $[23, 23, -w - 3]$ | $\phantom{-}1$ |
29 | $[29, 29, -w^{2} + 2w + 4]$ | $-\frac{5}{2}e^{4} + 3e^{3} + \frac{55}{2}e^{2} - \frac{31}{2}e - \frac{97}{2}$ |
31 | $[31, 31, 2w - 3]$ | $-2e^{4} + 3e^{3} + 23e^{2} - 18e - 43$ |
41 | $[41, 41, -2w^{2} + 3w + 6]$ | $\phantom{-}e^{4} - e^{3} - 12e^{2} + 5e + 22$ |
43 | $[43, 43, w^{2} - 3w + 3]$ | $-\frac{11}{4}e^{4} + 3e^{3} + \frac{127}{4}e^{2} - \frac{61}{4}e - \frac{257}{4}$ |
47 | $[47, 47, w^{2} + w - 4]$ | $\phantom{-}\frac{3}{4}e^{4} - e^{3} - \frac{35}{4}e^{2} + \frac{21}{4}e + \frac{57}{4}$ |
49 | $[49, 7, 2w^{2} - 3w - 3]$ | $\phantom{-}\frac{17}{4}e^{4} - 5e^{3} - \frac{197}{4}e^{2} + \frac{95}{4}e + \frac{395}{4}$ |
53 | $[53, 53, w^{2} - 3w - 2]$ | $-\frac{11}{4}e^{4} + 3e^{3} + \frac{127}{4}e^{2} - \frac{49}{4}e - \frac{265}{4}$ |
59 | $[59, 59, 2w^{2} - w - 5]$ | $-3e^{4} + 3e^{3} + 36e^{2} - 15e - 78$ |
59 | $[59, 59, w^{2} - w - 7]$ | $\phantom{-}4e^{4} - 6e^{3} - 43e^{2} + 33e + 75$ |
59 | $[59, 59, -w^{2} - w + 7]$ | $\phantom{-}\frac{9}{2}e^{4} - 5e^{3} - \frac{103}{2}e^{2} + \frac{51}{2}e + \frac{197}{2}$ |
67 | $[67, 67, 2w^{2} - 3w - 7]$ | $-\frac{19}{4}e^{4} + 6e^{3} + \frac{211}{4}e^{2} - \frac{125}{4}e - \frac{365}{4}$ |
73 | $[73, 73, -w^{2} + 4w - 5]$ | $\phantom{-}\frac{5}{2}e^{4} - 3e^{3} - \frac{53}{2}e^{2} + \frac{25}{2}e + \frac{99}{2}$ |
79 | $[79, 79, w^{2} - 8]$ | $\phantom{-}\frac{11}{4}e^{4} - 2e^{3} - \frac{131}{4}e^{2} + \frac{37}{4}e + \frac{261}{4}$ |
79 | $[79, 79, w^{2} - 5w + 5]$ | $-\frac{3}{2}e^{4} + 2e^{3} + \frac{31}{2}e^{2} - \frac{17}{2}e - \frac{53}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, -w - 3]$ | $-1$ |