Base field \(\Q(\sqrt{393}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 98\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[6, 6, -5w - 47]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} - 12x^{5} - x^{4} + 40x^{3} + 6x^{2} - 28x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -17w - 160]$ | $\phantom{-}e$ |
2 | $[2, 2, -17w + 177]$ | $-1$ |
3 | $[3, 3, -842w + 8767]$ | $-1$ |
7 | $[7, 7, -2w + 21]$ | $-\frac{1}{4}e^{6} + 3e^{4} - \frac{3}{4}e^{3} - 10e^{2} + \frac{9}{2}e + 6$ |
7 | $[7, 7, 2w + 19]$ | $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 6e + 1$ |
13 | $[13, 13, -12w - 113]$ | $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} + \frac{3}{4}e^{3} + 10e^{2} - \frac{9}{2}e - 7$ |
13 | $[13, 13, 12w - 125]$ | $\phantom{-}\frac{1}{4}e^{6} - 2e^{4} - \frac{5}{4}e^{3} + 3e^{2} + \frac{11}{2}e - 1$ |
17 | $[17, 17, 182w - 1895]$ | $-\frac{1}{4}e^{6} + \frac{1}{2}e^{5} + 3e^{4} - \frac{19}{4}e^{3} - \frac{19}{2}e^{2} + \frac{19}{2}e + 6$ |
17 | $[17, 17, 182w + 1713]$ | $-\frac{1}{4}e^{6} + 4e^{4} - \frac{3}{4}e^{3} - 16e^{2} + \frac{7}{2}e + 9$ |
23 | $[23, 23, -512w - 4819]$ | $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 8e + 1$ |
23 | $[23, 23, 512w - 5331]$ | $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} - \frac{1}{4}e^{3} + 11e^{2} + \frac{1}{2}e - 9$ |
25 | $[25, 5, -5]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 5e^{4} - \frac{7}{2}e^{3} - \frac{27}{2}e^{2} + 5e + 9$ |
29 | $[29, 29, 22w - 229]$ | $\phantom{-}\frac{3}{4}e^{6} - \frac{1}{2}e^{5} - 9e^{4} + \frac{17}{4}e^{3} + \frac{57}{2}e^{2} - \frac{15}{2}e - 12$ |
29 | $[29, 29, 22w + 207]$ | $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 4e + 4$ |
43 | $[43, 43, 114w + 1073]$ | $-\frac{1}{2}e^{6} + 5e^{4} + \frac{3}{2}e^{3} - 14e^{2} - 6e + 9$ |
43 | $[43, 43, 114w - 1187]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 4e^{4} + \frac{7}{2}e^{3} + \frac{17}{2}e^{2} - 5e - 13$ |
47 | $[47, 47, 8w - 83]$ | $\phantom{-}\frac{1}{4}e^{6} - 2e^{4} - \frac{1}{4}e^{3} + 2e^{2} - \frac{3}{2}e + 5$ |
47 | $[47, 47, -8w - 75]$ | $-\frac{1}{4}e^{6} + 3e^{4} - \frac{3}{4}e^{3} - 10e^{2} + \frac{5}{2}e + 10$ |
61 | $[61, 61, -1172w - 11031]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{2}e^{5} - 4e^{4} - \frac{13}{4}e^{3} + \frac{33}{2}e^{2} + \frac{3}{2}e - 12$ |
61 | $[61, 61, 1172w - 12203]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 6e^{4} - \frac{9}{2}e^{3} - \frac{41}{2}e^{2} + 7e + 17$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -17w + 177]$ | $1$ |
$3$ | $[3, 3, -842w + 8767]$ | $1$ |