Base field \(\Q(\zeta_{15})^+\)
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 4x^{2} + 4x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[121, 11, -w^{3} + 3w + 3]$ |
Dimension: | $6$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 24x^{4} + 112x^{2} - 64\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w^{2} + 1]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} + w^{2} - 4w - 3]$ | $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 3e$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 1$ |
29 | $[29, 29, -w^{3} - w^{2} + 2w + 3]$ | $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 12e$ |
29 | $[29, 29, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{4}e^{3} - 4e$ |
29 | $[29, 29, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 12e$ |
29 | $[29, 29, 2w^{3} + w^{2} - 7w]$ | $\phantom{-}\frac{1}{4}e^{3} - 4e$ |
31 | $[31, 31, -2w + 1]$ | $-\frac{1}{8}e^{4} + 2e^{2}$ |
31 | $[31, 31, 2w^{2} - 5]$ | $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 10$ |
31 | $[31, 31, 2w^{3} + 2w^{2} - 6w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 10$ |
31 | $[31, 31, 2w^{3} - 8w + 1]$ | $-\frac{1}{8}e^{4} + 2e^{2}$ |
59 | $[59, 59, w^{3} + w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} - 8e$ |
59 | $[59, 59, -w^{3} + 2w^{2} + 4w - 5]$ | $-\frac{3}{16}e^{5} + 4e^{3} - 13e$ |
59 | $[59, 59, -3w^{3} + 10w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} - 8e$ |
59 | $[59, 59, -2w^{3} - w^{2} + 7w - 2]$ | $-\frac{3}{16}e^{5} + 4e^{3} - 13e$ |
61 | $[61, 61, 4w^{3} + w^{2} - 13w - 1]$ | $-\frac{1}{4}e^{4} + 4e^{2} - 2$ |
61 | $[61, 61, 2w^{3} - w^{2} - 5w + 2]$ | $-\frac{1}{4}e^{4} + 4e^{2} - 2$ |
61 | $[61, 61, -3w^{3} - w^{2} + 8w]$ | $\phantom{-}\frac{1}{8}e^{4} - 3e^{2} + 8$ |
61 | $[61, 61, 3w^{3} - w^{2} - 10w + 5]$ | $\phantom{-}\frac{1}{8}e^{4} - 3e^{2} + 8$ |
89 | $[89, 89, w^{3} + w^{2} - w - 4]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + 4e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$121$ | $[121, 11, -w^{3} + 3w + 3]$ | $1$ |