Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[17, 17, -w^{2} + 2w + 1]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 4x^{4} - 14x^{3} + 72x^{2} - 56x - 24\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w^{3} + 2w^{2} + 3w]$ | $\phantom{-}e$ |
7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{1}{10}e^{4} - \frac{3}{10}e^{3} - \frac{17}{10}e^{2} + 5e - \frac{8}{5}$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{3}{5}e^{3} - \frac{17}{5}e^{2} + 10e - \frac{6}{5}$ |
13 | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $-\frac{1}{10}e^{4} + \frac{3}{10}e^{3} + \frac{11}{5}e^{2} - 4e - \frac{32}{5}$ |
16 | $[16, 2, 2]$ | $\phantom{-}e - 1$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ | $-\frac{7}{20}e^{4} + \frac{3}{10}e^{3} + \frac{31}{5}e^{2} - 7e - \frac{42}{5}$ |
17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $\phantom{-}\frac{3}{20}e^{4} - \frac{1}{5}e^{3} - \frac{23}{10}e^{2} + 4e - \frac{12}{5}$ |
17 | $[17, 17, -w^{2} + 2w + 1]$ | $-1$ |
19 | $[19, 19, w^{2} - w - 2]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{9}{2}e^{2} + 10e + 2$ |
29 | $[29, 29, w^{3} - 2w^{2} - 5w]$ | $\phantom{-}\frac{1}{20}e^{4} - \frac{2}{5}e^{3} - \frac{3}{5}e^{2} + 7e - \frac{24}{5}$ |
29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - 8e + 6$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{1}{10}e^{4} + \frac{3}{10}e^{3} + \frac{6}{5}e^{2} - 4e + \frac{28}{5}$ |
43 | $[43, 43, 2w^{3} - 3w^{2} - 11w]$ | $-\frac{9}{20}e^{4} + \frac{3}{5}e^{3} + \frac{37}{5}e^{2} - 11e - \frac{14}{5}$ |
47 | $[47, 47, w^{3} - 7w - 4]$ | $-\frac{1}{2}e^{3} + 8e$ |
53 | $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 8e^{2} - 12e$ |
61 | $[61, 61, -w - 3]$ | $\phantom{-}\frac{13}{20}e^{4} - \frac{7}{10}e^{3} - \frac{59}{5}e^{2} + 15e + \frac{88}{5}$ |
73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $-\frac{13}{20}e^{4} + \frac{6}{5}e^{3} + \frac{54}{5}e^{2} - 23e - \frac{8}{5}$ |
73 | $[73, 73, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}\frac{3}{5}e^{4} - \frac{13}{10}e^{3} - \frac{46}{5}e^{2} + 25e - \frac{38}{5}$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{7}{20}e^{4} - \frac{13}{10}e^{3} - \frac{31}{5}e^{2} + 23e - \frac{28}{5}$ |
83 | $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ | $\phantom{-}\frac{1}{20}e^{4} - \frac{2}{5}e^{3} - \frac{3}{5}e^{2} + 7e - \frac{24}{5}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{2} + 2w + 1]$ | $1$ |