Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[23, 23, -w^{2} + 3]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 12x^{3} + x^{2} + 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 1]$ | $-6e^{4} - 2e^{3} + 71e^{2} + 18e - 15$ |
7 | $[7, 7, -w + 2]$ | $\phantom{-}e^{4} - 12e^{2} + e + 6$ |
8 | $[8, 2, 2]$ | $-e + 1$ |
11 | $[11, 11, -w^{2} + 2w + 2]$ | $-2e^{4} + 24e^{2} - 2e - 5$ |
17 | $[17, 17, -w - 3]$ | $\phantom{-}8e^{4} + 3e^{3} - 95e^{2} - 27e + 25$ |
17 | $[17, 17, -w^{2} + 2w + 1]$ | $-4e^{4} - e^{3} + 48e^{2} + 8e - 12$ |
17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}2e^{4} - 24e^{2} + e + 6$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}1$ |
27 | $[27, 3, -3]$ | $-8e^{4} - 2e^{3} + 95e^{2} + 18e - 22$ |
29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}4e^{4} + e^{3} - 47e^{2} - 10e + 8$ |
29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}4e^{4} + e^{3} - 47e^{2} - 8e + 10$ |
29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}11e^{4} + 4e^{3} - 131e^{2} - 35e + 35$ |
31 | $[31, 31, w^{2} - 2]$ | $\phantom{-}21e^{4} + 8e^{3} - 249e^{2} - 74e + 61$ |
37 | $[37, 37, 2w - 5]$ | $-12e^{4} - 5e^{3} + 142e^{2} + 48e - 35$ |
43 | $[43, 43, w^{2} - 2w - 5]$ | $-12e^{4} - 4e^{3} + 142e^{2} + 34e - 28$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $-16e^{4} - 6e^{3} + 190e^{2} + 56e - 41$ |
49 | $[49, 7, w^{2} + w - 4]$ | $\phantom{-}18e^{4} + 6e^{3} - 213e^{2} - 51e + 46$ |
53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}13e^{4} + 4e^{3} - 155e^{2} - 36e + 38$ |
71 | $[71, 71, w - 5]$ | $-5e^{4} - 2e^{3} + 59e^{2} + 17e - 16$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, -w^{2} + 3]$ | $-1$ |