Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[10,10,-w + 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 3x^{4} - 9x^{3} - 23x^{2} + 16x + 20\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 6]$ | $\phantom{-}1$ |
3 | $[3, 3, w + 1]$ | $-\frac{1}{4}e^{3} + \frac{7}{4}e - \frac{3}{2}$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 2]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{9}{4}e^{2} + \frac{3}{4}e - \frac{5}{2}$ |
5 | $[5, 5, w + 3]$ | $-1$ |
11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{7}{4}e^{2} - 2e - 1$ |
11 | $[11, 11, w + 10]$ | $-\frac{1}{4}e^{3} - e^{2} + \frac{3}{4}e + \frac{5}{2}$ |
17 | $[17, 17, -3w + 17]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 1$ |
29 | $[29, 29, w + 11]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - \frac{5}{4}e^{2} - \frac{3}{4}e - \frac{7}{2}$ |
29 | $[29, 29, w + 18]$ | $\phantom{-}\frac{1}{4}e^{4} + e^{3} - \frac{3}{4}e^{2} - \frac{15}{2}e - 2$ |
37 | $[37, 37, w + 16]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{4}e^{3} - \frac{11}{2}e^{2} - \frac{21}{4}e + \frac{13}{2}$ |
37 | $[37, 37, w + 21]$ | $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{7}{4}e^{2} + 2e - 3$ |
47 | $[47, 47, -w - 9]$ | $\phantom{-}\frac{1}{4}e^{4} + 2e^{3} - \frac{1}{4}e^{2} - 12e - 1$ |
47 | $[47, 47, w - 9]$ | $-\frac{3}{4}e^{4} - \frac{3}{2}e^{3} + \frac{23}{4}e^{2} + \frac{17}{2}e - 6$ |
49 | $[49, 7, -7]$ | $\phantom{-}e^{2} + 2e - 4$ |
61 | $[61, 61, w + 20]$ | $-\frac{1}{2}e^{4} - \frac{5}{4}e^{3} + 2e^{2} + \frac{17}{4}e + \frac{11}{2}$ |
61 | $[61, 61, w + 41]$ | $-\frac{1}{2}e^{2} - \frac{7}{2}e + 1$ |
89 | $[89, 89, 2w - 15]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - 5e^{2} - 10e + 6$ |
89 | $[89, 89, -2w - 15]$ | $\phantom{-}\frac{1}{2}e^{4} - 8e^{2} - \frac{1}{2}e + 19$ |
103 | $[103, 103, -14w + 81]$ | $-\frac{1}{2}e^{4} - e^{3} + \frac{7}{2}e^{2} + 7e + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-w - 6]$ | $-1$ |
$5$ | $[5,5,-w + 2]$ | $1$ |