Base field 4.4.11197.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[21, 21, w^{3} - w^{2} - 5w]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 5x^{4} - 18x^{3} + 78x^{2} + 89x - 257\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $-1$ |
7 | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $-1$ |
11 | $[11, 11, -w - 2]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}e - 3$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{5}{4}e^{2} - \frac{9}{4}e + \frac{45}{4}$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{3}{4}e^{3} - e^{2} + \frac{29}{4}e + \frac{3}{8}$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{4}e^{2} - \frac{5}{4}e + \frac{51}{4}$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{13}{4}e - \frac{27}{4}$ |
23 | $[23, 23, -w^{2} + 3]$ | $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{17}{4}e - \frac{23}{4}$ |
27 | $[27, 3, w^{3} - 3w^{2} - w + 4]$ | $\phantom{-}\frac{1}{8}e^{4} - e^{3} + \frac{1}{4}e^{2} + \frac{19}{2}e - \frac{55}{8}$ |
29 | $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{13}{4}e + \frac{7}{4}$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $-\frac{1}{8}e^{4} + \frac{3}{4}e^{3} - \frac{21}{4}e + \frac{69}{8}$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ | $-\frac{1}{4}e^{4} + \frac{5}{4}e^{3} + \frac{9}{4}e^{2} - \frac{41}{4}e + 1$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}e^{2} - e - 12$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $-\frac{1}{8}e^{4} + \frac{1}{2}e^{3} + \frac{9}{4}e^{2} - 5e - \frac{77}{8}$ |
67 | $[67, 67, -w^{3} + w^{2} + 5w - 1]$ | $-\frac{1}{8}e^{4} + \frac{1}{2}e^{3} + \frac{5}{4}e^{2} - 5e + \frac{59}{8}$ |
67 | $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ | $\phantom{-}\frac{1}{4}e^{4} - e^{3} - \frac{7}{2}e^{2} + 9e + \frac{37}{4}$ |
83 | $[83, 83, -2w + 3]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{13}{4}e^{2} - \frac{31}{4}e + \frac{105}{4}$ |
89 | $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ | $-\frac{3}{4}e^{3} + \frac{13}{4}e^{2} + \frac{31}{4}e - \frac{101}{4}$ |
97 | $[97, 97, w^{3} - w^{2} - 4w - 3]$ | $-\frac{1}{8}e^{4} + e^{3} - \frac{1}{4}e^{2} - \frac{13}{2}e + \frac{47}{8}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $1$ |
$7$ | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $1$ |