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: | $[9, 3, 3]$ |
Dimension: | $20$ |
CM: | no |
Base change: | no |
Newspace dimension: | $104$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{20} - 29x^{18} + 347x^{16} - 2225x^{14} + 8342x^{12} - 18815x^{10} + 25408x^{8} - 19951x^{6} + 8687x^{4} - 1926x^{2} + 169\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -17w - 160]$ | $...$ |
2 | $[2, 2, -17w + 177]$ | $\phantom{-}e$ |
3 | $[3, 3, -842w + 8767]$ | $\phantom{-}0$ |
7 | $[7, 7, -2w + 21]$ | $-\frac{6065}{29858}e^{18} + \frac{87040}{14929}e^{16} - \frac{2054741}{29858}e^{14} + \frac{6467391}{14929}e^{12} - \frac{23638091}{14929}e^{10} + \frac{102811867}{29858}e^{8} - \frac{131280445}{29858}e^{6} + \frac{46846808}{14929}e^{4} - \frac{33840067}{29858}e^{2} + \frac{4654925}{29858}$ |
7 | $[7, 7, 2w + 19]$ | $...$ |
13 | $[13, 13, -12w - 113]$ | $...$ |
13 | $[13, 13, 12w - 125]$ | $...$ |
17 | $[17, 17, 182w - 1895]$ | $...$ |
17 | $[17, 17, 182w + 1713]$ | $...$ |
23 | $[23, 23, -512w - 4819]$ | $...$ |
23 | $[23, 23, 512w - 5331]$ | $...$ |
25 | $[25, 5, -5]$ | $...$ |
29 | $[29, 29, 22w - 229]$ | $...$ |
29 | $[29, 29, 22w + 207]$ | $...$ |
43 | $[43, 43, 114w + 1073]$ | $...$ |
43 | $[43, 43, 114w - 1187]$ | $...$ |
47 | $[47, 47, 8w - 83]$ | $...$ |
47 | $[47, 47, -8w - 75]$ | $...$ |
61 | $[61, 61, -1172w - 11031]$ | $...$ |
61 | $[61, 61, 1172w - 12203]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -842w + 8767]$ | $-1$ |