Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16,4,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 8]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 13x^{3} + 25x^{2} - 2x - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ | $\phantom{-}0$ |
9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ | $-\frac{3}{2}e^{4} - \frac{1}{2}e^{3} + \frac{37}{2}e^{2} - \frac{25}{2}e - 10$ |
9 | $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ | $\phantom{-}e^{4} + e^{3} - 12e^{2} + 2e + 11$ |
11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ | $\phantom{-}3e^{4} + e^{3} - 38e^{2} + 25e + 27$ |
11 | $[11, 11, -w - 3]$ | $-e^{4} + 13e^{2} - 12e - 8$ |
25 | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $\phantom{-}4e^{4} + e^{3} - 51e^{2} + 35e + 35$ |
29 | $[29, 29, w + 1]$ | $\phantom{-}4e^{4} + e^{3} - 51e^{2} + 35e + 36$ |
29 | $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ | $-\frac{3}{2}e^{4} - \frac{1}{2}e^{3} + \frac{39}{2}e^{2} - \frac{23}{2}e - 16$ |
31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ | $-\frac{13}{2}e^{4} - \frac{5}{2}e^{3} + \frac{161}{2}e^{2} - \frac{99}{2}e - 55$ |
31 | $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ | $-2e + 2$ |
31 | $[31, 31, -w + 3]$ | $-5e^{4} - 2e^{3} + 62e^{2} - 38e - 37$ |
31 | $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - \frac{37}{2}e^{2} + \frac{27}{2}e + 16$ |
59 | $[59, 59, 2w^{2} - w - 13]$ | $-e^{4} + 13e^{2} - 10e$ |
59 | $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ | $-10e^{4} - 4e^{3} + 125e^{2} - 76e - 89$ |
61 | $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ | $\phantom{-}\frac{7}{2}e^{4} + \frac{3}{2}e^{3} - \frac{87}{2}e^{2} + \frac{49}{2}e + 36$ |
61 | $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ | $-3e^{4} - 2e^{3} + 37e^{2} - 14e - 29$ |
71 | $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ | $\phantom{-}\frac{7}{2}e^{4} + \frac{1}{2}e^{3} - \frac{91}{2}e^{2} + \frac{63}{2}e + 41$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ | $\phantom{-}\frac{21}{2}e^{4} + \frac{9}{2}e^{3} - \frac{259}{2}e^{2} + \frac{155}{2}e + 88$ |
79 | $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ | $-\frac{19}{2}e^{4} - \frac{9}{2}e^{3} + \frac{233}{2}e^{2} - \frac{131}{2}e - 80$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 10]$ | $1$ |