Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[2, 2, w^{2}]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 19x^{4} + 75x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{2}]$ | $\phantom{-}\frac{1}{36}e^{5} + \frac{11}{18}e^{3} + \frac{35}{12}e$ |
4 | $[4, 2, w^{2} + w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{12}e^{5} + \frac{4}{3}e^{3} + \frac{13}{4}e$ |
11 | $[11, 11, 10w + 4]$ | $-\frac{1}{4}e^{5} - \frac{9}{2}e^{3} - \frac{65}{4}e$ |
13 | $[13, 13, 12w^{2} + w + 7]$ | $-\frac{1}{4}e^{5} - \frac{9}{2}e^{3} - \frac{65}{4}e$ |
17 | $[17, 17, w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{9}{2}$ |
17 | $[17, 17, 16w^{2} + 16]$ | $\phantom{-}\frac{1}{12}e^{5} + \frac{11}{6}e^{3} + \frac{31}{4}e$ |
17 | $[17, 17, 16w^{2} + 16w + 8]$ | $\phantom{-}\frac{1}{6}e^{5} + \frac{19}{6}e^{3} + 13e$ |
19 | $[19, 19, 18w^{2} + 18w + 1]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{19}{3}e^{3} + 24e$ |
19 | $[19, 19, -w^{2} + 7]$ | $-\frac{1}{4}e^{4} - \frac{7}{2}e^{2} - \frac{13}{4}$ |
25 | $[25, 5, 4w^{2} + w + 4]$ | $\phantom{-}\frac{1}{4}e^{5} + 5e^{3} + \frac{83}{4}e$ |
27 | $[27, 3, -3]$ | $-\frac{1}{4}e^{4} - \frac{7}{2}e^{2} - \frac{29}{4}$ |
29 | $[29, 29, w + 7]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{13}{2}e$ |
41 | $[41, 41, 40w^{2} + 18]$ | $-2e$ |
43 | $[43, 43, w^{2} - 11]$ | $-8$ |
47 | $[47, 47, 2w^{2} + 2w - 13]$ | $\phantom{-}e^{2} + 3$ |
59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{5}{2}e^{2} + \frac{9}{4}$ |
73 | $[73, 73, w^{2} + 2w - 1]$ | $\phantom{-}\frac{1}{4}e^{4} + 5e^{2} + \frac{67}{4}$ |
79 | $[79, 79, w^{2} + 37]$ | $-\frac{5}{12}e^{5} - \frac{49}{6}e^{3} - \frac{127}{4}e$ |
97 | $[97, 97, w^{2} + 2w - 7]$ | $\phantom{-}\frac{1}{4}e^{4} + 4e^{2} + \frac{7}{4}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{2}]$ | $-\frac{1}{36}e^{5} - \frac{11}{18}e^{3} - \frac{35}{12}e$ |