Base field \(\Q(\sqrt{29}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 7\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[45, 15, 3w + 3]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 12x^{3} - 3x^{2} + 30x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}1$ |
5 | $[5, 5, w - 2]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 4e^{2} + \frac{9}{2}e + 4$ |
7 | $[7, 7, w]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 3e^{2} + \frac{11}{2}e$ |
7 | $[7, 7, -w + 1]$ | $-e^{2} + e + 4$ |
9 | $[9, 3, 3]$ | $\phantom{-}1$ |
13 | $[13, 13, w + 4]$ | $\phantom{-}e^{4} - 2e^{3} - 7e^{2} + 10e + 4$ |
13 | $[13, 13, w - 5]$ | $-\frac{1}{2}e^{4} + 5e^{2} + \frac{1}{2}e - 5$ |
23 | $[23, 23, -w - 5]$ | $-e^{4} + 2e^{3} + 8e^{2} - 11e - 10$ |
23 | $[23, 23, w - 6]$ | $-\frac{1}{2}e^{4} + 2e^{3} + 2e^{2} - \frac{21}{2}e + 5$ |
29 | $[29, 29, 2w - 1]$ | $-\frac{1}{2}e^{4} + e^{3} + 4e^{2} - \frac{13}{2}e - 6$ |
53 | $[53, 53, 3w - 5]$ | $-\frac{1}{2}e^{4} + 2e^{3} + 4e^{2} - \frac{25}{2}e - 5$ |
53 | $[53, 53, -3w - 2]$ | $-2e^{3} + 2e^{2} + 14e - 8$ |
59 | $[59, 59, -3w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 3e^{3} + \frac{37}{2}e - 6$ |
59 | $[59, 59, 3w - 4]$ | $-\frac{1}{2}e^{4} + 2e^{3} + 2e^{2} - \frac{25}{2}e + 3$ |
67 | $[67, 67, 3w - 13]$ | $\phantom{-}e^{4} - 4e^{3} - 5e^{2} + 24e - 4$ |
67 | $[67, 67, -3w - 10]$ | $-e^{4} + 2e^{3} + 7e^{2} - 12e - 8$ |
71 | $[71, 71, 2w - 11]$ | $\phantom{-}\frac{1}{2}e^{4} - 6e^{2} - \frac{7}{2}e + 11$ |
71 | $[71, 71, -2w - 9]$ | $-\frac{1}{2}e^{4} + 4e^{2} + \frac{7}{2}e - 9$ |
83 | $[83, 83, -w - 9]$ | $-\frac{1}{2}e^{4} + 3e^{3} + 2e^{2} - \frac{37}{2}e + 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w + 1]$ | $-1$ |
$9$ | $[9, 3, 3]$ | $-1$ |