Base field 4.4.14197.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9, 3, w^{3} - 5w - 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 7x^{4} + 5x^{3} + 50x^{2} - 113x + 68\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} - 5w - 2]$ | $-1$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}6e^{4} - 33e^{3} - 19e^{2} + 270e - 274$ |
13 | $[13, 13, -w + 2]$ | $-6e^{4} + 33e^{3} + 19e^{2} - 270e + 278$ |
16 | $[16, 2, 2]$ | $\phantom{-}e^{4} - 5e^{3} - 5e^{2} + 39e - 31$ |
17 | $[17, 17, w^{3} - w^{2} - 5w]$ | $-e^{4} + 5e^{3} + 5e^{2} - 40e + 34$ |
19 | $[19, 19, -w^{3} + w^{2} + 6w]$ | $-7e^{4} + 39e^{3} + 20e^{2} - 319e + 336$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $-7e^{4} + 39e^{3} + 21e^{2} - 321e + 332$ |
29 | $[29, 29, w^{3} - 5w]$ | $\phantom{-}16e^{4} - 89e^{3} - 48e^{2} + 731e - 754$ |
31 | $[31, 31, w^{3} - 6w - 1]$ | $-7e^{4} + 39e^{3} + 21e^{2} - 320e + 332$ |
31 | $[31, 31, w^{2} - 2]$ | $-12e^{4} + 67e^{3} + 35e^{2} - 552e + 576$ |
37 | $[37, 37, -w - 3]$ | $\phantom{-}e^{4} - 5e^{3} - 4e^{2} + 40e - 42$ |
37 | $[37, 37, w^{3} - 4w - 1]$ | $\phantom{-}11e^{4} - 61e^{3} - 34e^{2} + 500e - 510$ |
37 | $[37, 37, w^{3} - 7w - 4]$ | $\phantom{-}13e^{4} - 73e^{3} - 37e^{2} + 603e - 630$ |
37 | $[37, 37, w^{2} - 3]$ | $\phantom{-}8e^{4} - 45e^{3} - 23e^{2} + 370e - 378$ |
43 | $[43, 43, w^{2} + w - 3]$ | $-8e^{4} + 45e^{3} + 22e^{2} - 371e + 392$ |
43 | $[43, 43, w^{3} - w^{2} - 5w - 1]$ | $-13e^{4} + 73e^{3} + 37e^{2} - 600e + 628$ |
47 | $[47, 47, -w^{3} + w^{2} + 5w - 4]$ | $-10e^{4} + 54e^{3} + 35e^{2} - 443e + 444$ |
53 | $[53, 53, w^{3} - 6w]$ | $-15e^{4} + 83e^{3} + 47e^{2} - 681e + 698$ |
61 | $[61, 61, w^{3} - w^{2} - 7w - 2]$ | $\phantom{-}2e^{4} - 11e^{3} - 7e^{2} + 93e - 94$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, w^{3} - 5w - 2]$ | $1$ |