Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, -w^{2} + w + 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 4x^{5} - 31x^{4} - 128x^{3} + 126x^{2} + 918x + 864\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $-1$ |
5 | $[5, 5, -w + 2]$ | $-1$ |
11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $-\frac{19}{54}e^{5} - \frac{17}{27}e^{4} + \frac{667}{54}e^{3} + \frac{493}{27}e^{2} - \frac{767}{9}e - \frac{431}{3}$ |
16 | $[16, 2, 2]$ | $-\frac{25}{27}e^{5} - \frac{40}{27}e^{4} + \frac{871}{27}e^{3} + \frac{1115}{27}e^{2} - \frac{1933}{9}e - \frac{1003}{3}$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}\frac{17}{54}e^{5} + \frac{10}{27}e^{4} - \frac{593}{54}e^{3} - \frac{254}{27}e^{2} + \frac{640}{9}e + \frac{271}{3}$ |
19 | $[19, 19, w^{3} - 5w]$ | $-2e^{5} - \frac{10}{3}e^{4} + \frac{209}{3}e^{3} + \frac{280}{3}e^{2} - \frac{1399}{3}e - 744$ |
19 | $[19, 19, -w + 3]$ | $-\frac{37}{18}e^{5} - \frac{29}{9}e^{4} + \frac{1291}{18}e^{3} + \frac{802}{9}e^{2} - 479e - 731$ |
23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $-\frac{22}{27}e^{5} - \frac{37}{27}e^{4} + \frac{769}{27}e^{3} + \frac{1037}{27}e^{2} - \frac{1729}{9}e - \frac{910}{3}$ |
23 | $[23, 23, w^{2} - 2]$ | $-\frac{89}{54}e^{5} - \frac{73}{27}e^{4} + \frac{3095}{54}e^{3} + \frac{2027}{27}e^{2} - \frac{3439}{9}e - \frac{1801}{3}$ |
25 | $[25, 5, w^{2} - 3]$ | $-\frac{25}{27}e^{5} - \frac{40}{27}e^{4} + \frac{871}{27}e^{3} + \frac{1115}{27}e^{2} - \frac{1942}{9}e - \frac{1012}{3}$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $-\frac{3}{2}e^{5} - \frac{7}{3}e^{4} + \frac{313}{6}e^{3} + \frac{193}{3}e^{2} - \frac{1036}{3}e - 525$ |
37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $\phantom{-}\frac{61}{54}e^{5} + \frac{47}{27}e^{4} - \frac{2131}{54}e^{3} - \frac{1291}{27}e^{2} + \frac{2387}{9}e + \frac{1187}{3}$ |
41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{68}{27}e^{5} - \frac{107}{27}e^{4} + \frac{2372}{27}e^{3} + \frac{2977}{27}e^{2} - \frac{5282}{9}e - \frac{2708}{3}$ |
47 | $[47, 47, w^{3} - 6w + 1]$ | $-\frac{5}{6}e^{5} - \frac{4}{3}e^{4} + \frac{173}{6}e^{3} + \frac{110}{3}e^{2} - 190e - 297$ |
61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{31}{27}e^{5} + \frac{46}{27}e^{4} - \frac{1075}{27}e^{3} - \frac{1244}{27}e^{2} + \frac{2350}{9}e + \frac{1150}{3}$ |
67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $\phantom{-}\frac{47}{18}e^{5} + \frac{40}{9}e^{4} - \frac{1637}{18}e^{3} - \frac{1118}{9}e^{2} + 611e + 979$ |
67 | $[67, 67, w^{3} - 7w + 3]$ | $\phantom{-}\frac{29}{18}e^{5} + \frac{22}{9}e^{4} - \frac{1007}{18}e^{3} - \frac{596}{9}e^{2} + 369e + 541$ |
73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $-\frac{17}{27}e^{5} - \frac{29}{27}e^{4} + \frac{584}{27}e^{3} + \frac{787}{27}e^{2} - \frac{1274}{9}e - \frac{668}{3}$ |
81 | $[81, 3, -3]$ | $-\frac{1}{18}e^{5} + \frac{1}{9}e^{4} + \frac{37}{18}e^{3} - \frac{29}{9}e^{2} - \frac{41}{3}e - 1$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w + 1]$ | $1$ |
$5$ | $[5, 5, -w + 2]$ | $1$ |