Base field 4.4.5725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ |
Dimension: | $7$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} - 35x^{5} - 2x^{4} + 360x^{3} - 104x^{2} - 1184x + 896\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ | $\phantom{-}e$ |
9 | $[9, 3, -w + 1]$ | $\phantom{-}e$ |
11 | $[11, 11, w]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 5$ |
11 | $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{1}{4}e^{4} - \frac{23}{8}e^{3} + 4e^{2} + \frac{27}{2}e - 17$ |
11 | $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 5$ |
11 | $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{1}{4}e^{4} - \frac{23}{8}e^{3} + 4e^{2} + \frac{27}{2}e - 17$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{32}e^{6} - \frac{1}{8}e^{5} - \frac{19}{32}e^{4} + \frac{45}{16}e^{3} + \frac{1}{2}e^{2} - \frac{65}{4}e + 20$ |
25 | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ | $-1$ |
29 | $[29, 29, -w - 3]$ | $-\frac{1}{16}e^{6} + \frac{27}{16}e^{4} + \frac{9}{8}e^{3} - 11e^{2} - \frac{17}{2}e + 20$ |
29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ | $-\frac{1}{16}e^{6} + \frac{27}{16}e^{4} + \frac{9}{8}e^{3} - 11e^{2} - \frac{17}{2}e + 20$ |
31 | $[31, 31, w^{3} - 6w + 1]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{4}e^{5} - \frac{23}{16}e^{4} + \frac{45}{8}e^{3} + \frac{25}{4}e^{2} - \frac{61}{2}e + 17$ |
31 | $[31, 31, w^{3} - 6w - 2]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{4}e^{5} - \frac{23}{16}e^{4} + \frac{45}{8}e^{3} + \frac{25}{4}e^{2} - \frac{61}{2}e + 17$ |
41 | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{25}{4}e^{3} + \frac{13}{4}e^{2} + 31e - 21$ |
41 | $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{25}{4}e^{3} + \frac{13}{4}e^{2} + 31e - 21$ |
59 | $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ | $-\frac{1}{8}e^{6} + \frac{27}{8}e^{4} + \frac{7}{4}e^{3} - \frac{41}{2}e^{2} - 9e + 24$ |
59 | $[59, 59, w^{3} + w^{2} - 6w - 4]$ | $-\frac{1}{8}e^{6} + \frac{27}{8}e^{4} + \frac{7}{4}e^{3} - \frac{41}{2}e^{2} - 9e + 24$ |
79 | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $-\frac{1}{16}e^{6} + \frac{1}{4}e^{5} + \frac{27}{16}e^{4} - \frac{49}{8}e^{3} - 11e^{2} + \frac{67}{2}e - 4$ |
79 | $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ | $-\frac{1}{16}e^{6} + \frac{1}{4}e^{5} + \frac{27}{16}e^{4} - \frac{49}{8}e^{3} - 11e^{2} + \frac{67}{2}e - 4$ |
89 | $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{2}e^{5} - \frac{19}{16}e^{4} + \frac{95}{8}e^{3} + 4e^{2} - \frac{121}{2}e + 28$ |
89 | $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{2}e^{5} - \frac{19}{16}e^{4} + \frac{95}{8}e^{3} + 4e^{2} - \frac{121}{2}e + 28$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ | $1$ |