Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[49, 7, 7]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $151$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - x^{2} - 5x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
7 | $[7, 7, w - 7]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 6]$ | $\phantom{-}1$ |
9 | $[9, 3, 3]$ | $-\frac{1}{2}e^{2} + e - \frac{1}{2}$ |
19 | $[19, 19, w + 5]$ | $-e + 5$ |
19 | $[19, 19, w - 6]$ | $-\frac{3}{2}e^{2} + 2e + \frac{7}{2}$ |
23 | $[23, 23, w + 8]$ | $\phantom{-}e^{2} - 5$ |
23 | $[23, 23, -w + 9]$ | $\phantom{-}e^{2} + 1$ |
25 | $[25, 5, 5]$ | $\phantom{-}e^{2} - 3e - 4$ |
29 | $[29, 29, -w - 4]$ | $-e - 5$ |
29 | $[29, 29, w - 5]$ | $-e + 7$ |
37 | $[37, 37, -w - 3]$ | $-e + 5$ |
37 | $[37, 37, w - 4]$ | $-4e + 2$ |
41 | $[41, 41, -w - 9]$ | $\phantom{-}e^{2} - e + 6$ |
41 | $[41, 41, w - 10]$ | $\phantom{-}e^{2} + 2e - 9$ |
43 | $[43, 43, -w - 2]$ | $-\frac{5}{2}e^{2} + e + \frac{23}{2}$ |
43 | $[43, 43, w - 3]$ | $\phantom{-}2e^{2} - 5e - 5$ |
47 | $[47, 47, -w - 1]$ | $\phantom{-}e^{2} - 2e - 3$ |
47 | $[47, 47, w - 2]$ | $\phantom{-}e^{2} - 2e + 3$ |
53 | $[53, 53, 2w - 13]$ | $-\frac{3}{2}e^{2} + 3e - \frac{3}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, w - 7]$ | $-1$ |
$7$ | $[7, 7, w + 6]$ | $-1$ |