Base field 4.4.19773.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} - 9x + 3\); narrow class number \(4\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 100x^{6} + 3344x^{4} - 44800x^{2} + 200704\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w^{3} - 2w^{2} - 8w - 3]$ | $\phantom{-}\frac{5}{2688}e^{6} - \frac{97}{672}e^{4} + \frac{527}{168}e^{2} - \frac{62}{3}$ |
3 | $[3, 3, w^{3} - 3w^{2} - 5w + 2]$ | $\phantom{-}\frac{3}{896}e^{6} - \frac{61}{224}e^{4} + \frac{347}{56}e^{2} - 40$ |
13 | $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ | $\phantom{-}1$ |
16 | $[16, 2, 2]$ | $-\frac{1}{192}e^{6} + \frac{5}{12}e^{4} - \frac{28}{3}e^{2} + \frac{167}{3}$ |
17 | $[17, 17, -2w^{3} + 5w^{2} + 14w - 1]$ | $\phantom{-}e$ |
17 | $[17, 17, -w^{3} + 3w^{2} + 5w - 4]$ | $-\frac{5}{5376}e^{7} + \frac{97}{1344}e^{5} - \frac{485}{336}e^{3} + \frac{19}{3}e$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 8w + 1]$ | $-e$ |
17 | $[17, 17, w - 1]$ | $\phantom{-}\frac{5}{5376}e^{7} - \frac{97}{1344}e^{5} + \frac{485}{336}e^{3} - \frac{19}{3}e$ |
23 | $[23, 23, 2w^{3} - 6w^{2} - 11w + 7]$ | $\phantom{-}\frac{13}{10752}e^{7} - \frac{269}{2688}e^{5} + \frac{1597}{672}e^{3} - \frac{101}{6}e$ |
23 | $[23, 23, w^{3} - 3w^{2} - 7w + 4]$ | $-\frac{13}{10752}e^{7} + \frac{269}{2688}e^{5} - \frac{1597}{672}e^{3} + \frac{101}{6}e$ |
23 | $[23, 23, -w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{5376}e^{7} - \frac{11}{1344}e^{5} - \frac{29}{336}e^{3} + \frac{17}{6}e$ |
23 | $[23, 23, 3w^{3} - 8w^{2} - 20w + 5]$ | $-\frac{1}{5376}e^{7} + \frac{11}{1344}e^{5} + \frac{29}{336}e^{3} - \frac{17}{6}e$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 9w + 1]$ | $-\frac{1}{336}e^{6} + \frac{43}{168}e^{4} - \frac{535}{84}e^{2} + \frac{116}{3}$ |
61 | $[61, 61, -2w^{3} + 5w^{2} + 13w - 2]$ | $-\frac{1}{448}e^{6} + \frac{9}{56}e^{4} - \frac{83}{28}e^{2} + 8$ |
61 | $[61, 61, w^{3} - 2w^{2} - 9w - 2]$ | $-\frac{1}{336}e^{6} + \frac{43}{168}e^{4} - \frac{535}{84}e^{2} + \frac{116}{3}$ |
61 | $[61, 61, 2w^{3} - 5w^{2} - 13w + 1]$ | $-\frac{1}{448}e^{6} + \frac{9}{56}e^{4} - \frac{83}{28}e^{2} + 8$ |
79 | $[79, 79, 4w^{3} - 10w^{2} - 28w + 5]$ | $\phantom{-}\frac{1}{2688}e^{6} - \frac{53}{672}e^{4} + \frac{559}{168}e^{2} - \frac{88}{3}$ |
79 | $[79, 79, w^{3} - 3w^{2} - 4w + 4]$ | $\phantom{-}\frac{1}{2688}e^{6} - \frac{53}{672}e^{4} + \frac{559}{168}e^{2} - \frac{88}{3}$ |
79 | $[79, 79, w^{3} - 4w^{2} - 2w + 10]$ | $-\frac{5}{896}e^{6} + \frac{111}{224}e^{4} - \frac{709}{56}e^{2} + 90$ |
79 | $[79, 79, 2w^{3} - 6w^{2} - 10w + 5]$ | $-\frac{5}{896}e^{6} + \frac{111}{224}e^{4} - \frac{709}{56}e^{2} + 90$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ | $-1$ |