Base field 6.6.703493.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[43,43,w^{5} - 7w^{3} - w^{2} + 10w + 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 8x^{3} + 11x^{2} - 42x - 89\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
13 | $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ | $-\frac{1}{2}e^{3} - 3e^{2} + e + \frac{35}{2}$ |
13 | $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ | $-2e^{3} - 9e^{2} + 9e + 50$ |
13 | $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ | $\phantom{-}\frac{3}{2}e^{3} + 7e^{2} - 7e - \frac{91}{2}$ |
13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}e$ |
41 | $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ | $-2e^{3} - 11e^{2} + 5e + 64$ |
41 | $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{7}{2}e - 10$ |
41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $-2e^{3} - \frac{17}{2}e^{2} + \frac{21}{2}e + \frac{95}{2}$ |
41 | $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ | $\phantom{-}\frac{5}{2}e^{3} + \frac{27}{2}e^{2} - \frac{19}{2}e - 85$ |
43 | $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ | $\phantom{-}\frac{5}{2}e^{3} + 14e^{2} - 8e - \frac{169}{2}$ |
43 | $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ | $\phantom{-}1$ |
49 | $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ | $\phantom{-}3e^{3} + \frac{29}{2}e^{2} - \frac{21}{2}e - \frac{167}{2}$ |
64 | $[64, 2, -2]$ | $\phantom{-}2e^{3} + \frac{17}{2}e^{2} - \frac{21}{2}e - \frac{101}{2}$ |
71 | $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ | $-\frac{9}{2}e^{3} - 22e^{2} + 18e + \frac{265}{2}$ |
71 | $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ | $\phantom{-}e^{3} + 3e^{2} - 8e - 16$ |
83 | $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{15}{2}e^{2} - \frac{7}{2}e - 44$ |
83 | $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ | $-5e^{3} - \frac{45}{2}e^{2} + \frac{49}{2}e + \frac{259}{2}$ |
97 | $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ | $\phantom{-}\frac{9}{2}e^{3} + 22e^{2} - 19e - \frac{267}{2}$ |
97 | $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ | $-\frac{11}{2}e^{3} - 26e^{2} + 21e + \frac{297}{2}$ |
113 | $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ | $-\frac{3}{2}e^{3} - 7e^{2} + 7e + \frac{77}{2}$ |
113 | $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ | $\phantom{-}3e^{3} + \frac{27}{2}e^{2} - \frac{25}{2}e - \frac{149}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$43$ | $[43,43,w^{5} - 7w^{3} - w^{2} + 10w + 3]$ | $-1$ |