Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, -w + 2]$ |
Dimension: | $8$ |
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:
\(x^{8} - 21x^{6} + 134x^{4} - 288x^{2} + 196\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $\phantom{-}\frac{2}{7}e^{7} - \frac{11}{2}e^{5} + \frac{403}{14}e^{3} - \frac{233}{7}e$ |
11 | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + 49e^{2} - 55$ |
13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}e$ |
13 | $[13, 13, -w + 2]$ | $-1$ |
17 | $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{3}{14}e^{7} + 4e^{5} - \frac{283}{14}e^{3} + \frac{166}{7}e$ |
19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + 49e^{2} - 56$ |
19 | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{1}{7}e^{7} - 3e^{5} + \frac{127}{7}e^{3} - \frac{190}{7}e$ |
23 | $[23, 23, w^{2} - 2w - 1]$ | $\phantom{-}\frac{5}{14}e^{7} - 7e^{5} + \frac{523}{14}e^{3} - \frac{293}{7}e$ |
27 | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $-\frac{4}{7}e^{7} + 11e^{5} - \frac{403}{7}e^{3} + \frac{459}{7}e$ |
29 | $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{14}e^{7} - \frac{3}{2}e^{5} + \frac{67}{7}e^{3} - \frac{130}{7}e$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ | $-\frac{1}{2}e^{7} + \frac{19}{2}e^{5} - 49e^{3} + 58e$ |
41 | $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ | $\phantom{-}\frac{5}{7}e^{7} - 14e^{5} + \frac{530}{7}e^{3} - \frac{649}{7}e$ |
53 | $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + 48e^{2} - 48$ |
59 | $[59, 59, w - 4]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + 47e^{2} - 50$ |
67 | $[67, 67, 2w^{2} - 3w - 8]$ | $\phantom{-}e^{4} - 12e^{2} + 21$ |
73 | $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ | $\phantom{-}\frac{13}{14}e^{7} - 18e^{5} + \frac{1329}{14}e^{3} - \frac{787}{7}e$ |
89 | $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ | $-\frac{2}{7}e^{7} + \frac{11}{2}e^{5} - \frac{403}{14}e^{3} + \frac{233}{7}e$ |
97 | $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ | $-\frac{1}{2}e^{6} + \frac{19}{2}e^{4} - 50e^{2} + 53$ |
97 | $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ | $-\frac{9}{14}e^{7} + \frac{25}{2}e^{5} - \frac{456}{7}e^{3} + \frac{470}{7}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w + 2]$ | $1$ |