Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[9, 3, 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 8x^{2} - 6x + 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 6]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 5]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e - \frac{1}{3}$ |
7 | $[7, 7, 6w - 35]$ | $-\frac{2}{3}e^{3} + e^{2} + \frac{13}{3}e - \frac{10}{3}$ |
7 | $[7, 7, -6w - 29]$ | $-e^{2} - e + 5$ |
9 | $[9, 3, 3]$ | $-1$ |
11 | $[11, 11, 4w + 19]$ | $\phantom{-}\frac{2}{3}e^{3} - e^{2} - \frac{10}{3}e + \frac{16}{3}$ |
11 | $[11, 11, 4w - 23]$ | $\phantom{-}\frac{1}{3}e^{3} + e^{2} - \frac{5}{3}e - \frac{10}{3}$ |
13 | $[13, 13, -2w + 11]$ | $\phantom{-}\frac{1}{3}e^{3} - e^{2} + \frac{1}{3}e + \frac{20}{3}$ |
13 | $[13, 13, 2w + 9]$ | $\phantom{-}\frac{2}{3}e^{3} + e^{2} - \frac{16}{3}e - \frac{8}{3}$ |
25 | $[25, 5, -5]$ | $\phantom{-}e^{3} - 5e + 1$ |
31 | $[31, 31, 2w - 13]$ | $-\frac{4}{3}e^{3} + e^{2} + \frac{26}{3}e - \frac{5}{3}$ |
31 | $[31, 31, -2w - 11]$ | $-\frac{1}{3}e^{3} - e^{2} - \frac{1}{3}e + \frac{19}{3}$ |
41 | $[41, 41, -8w - 39]$ | $-e^{3} - e^{2} + 6e - 1$ |
41 | $[41, 41, 8w - 47]$ | $-e^{3} + e^{2} + 4e - 10$ |
53 | $[53, 53, -26w - 125]$ | $-\frac{5}{3}e^{3} + \frac{22}{3}e + \frac{2}{3}$ |
53 | $[53, 53, 26w - 151]$ | $-2e^{3} + 11e + 1$ |
61 | $[61, 61, -14w + 81]$ | $\phantom{-}\frac{2}{3}e^{3} + e^{2} - \frac{16}{3}e - \frac{11}{3}$ |
61 | $[61, 61, -14w - 67]$ | $\phantom{-}\frac{1}{3}e^{3} - e^{2} + \frac{1}{3}e + \frac{17}{3}$ |
83 | $[83, 83, 2w - 15]$ | $\phantom{-}\frac{1}{3}e^{3} + 3e^{2} - \frac{8}{3}e - \frac{37}{3}$ |
83 | $[83, 83, -2w - 13]$ | $\phantom{-}e^{3} - 3e^{2} - 4e + 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, 3]$ | $1$ |