Base field \(\Q(\sqrt{389}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 97\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $98$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 5x^{9} - 25x^{8} + 136x^{7} + 168x^{6} - 1098x^{5} - 268x^{4} + 2753x^{3} + 737x^{2} - 2406x - 1237\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, -3w - 28]$ | $...$ |
| 5 | $[5, 5, -3w + 31]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w - 9]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 10]$ | $...$ |
| 9 | $[9, 3, 3]$ | $-1$ |
| 11 | $[11, 11, -2w - 19]$ | $...$ |
| 11 | $[11, 11, 2w - 21]$ | $...$ |
| 13 | $[13, 13, w - 11]$ | $...$ |
| 13 | $[13, 13, -w - 10]$ | $...$ |
| 17 | $[17, 17, -8w - 75]$ | $...$ |
| 17 | $[17, 17, -8w + 83]$ | $...$ |
| 19 | $[19, 19, -5w + 52]$ | $...$ |
| 19 | $[19, 19, 5w + 47]$ | $...$ |
| 41 | $[41, 41, -w - 7]$ | $...$ |
| 41 | $[41, 41, w - 8]$ | $-\frac{53465}{192047}e^{9} + \frac{1051191}{960235}e^{8} + \frac{7455536}{960235}e^{7} - \frac{26986498}{960235}e^{6} - \frac{64277971}{960235}e^{5} + \frac{188752754}{960235}e^{4} + \frac{39484689}{192047}e^{3} - \frac{271592464}{960235}e^{2} - \frac{290331226}{960235}e - \frac{43942763}{960235}$ |
| 59 | $[59, 59, -w - 12]$ | $...$ |
| 59 | $[59, 59, w - 13]$ | $...$ |
| 67 | $[67, 67, -w - 5]$ | $-\frac{107431}{960235}e^{9} + \frac{88951}{960235}e^{8} + \frac{885269}{192047}e^{7} - \frac{392069}{192047}e^{6} - \frac{62765161}{960235}e^{5} + \frac{6164853}{960235}e^{4} + \frac{340628389}{960235}e^{3} + \frac{66413978}{960235}e^{2} - \frac{510666354}{960235}e - \frac{290304166}{960235}$ |
| 67 | $[67, 67, w - 6]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $1$ |