Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15,15,-w + 3]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $100$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + x^{10} - 22x^{9} - 21x^{8} + 171x^{7} + 157x^{6} - 560x^{5} - 488x^{4} + 704x^{3} + 540x^{2} - 224x - 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, -w + 8]$ | $-1$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 13 | $[13, 13, w + 3]$ | $...$ |
| 13 | $[13, 13, w + 9]$ | $...$ |
| 17 | $[17, 17, w]$ | $...$ |
| 17 | $[17, 17, w + 16]$ | $-\frac{3013}{204244}e^{10} - \frac{4239}{204244}e^{9} + \frac{18784}{51061}e^{8} + \frac{87813}{204244}e^{7} - \frac{701157}{204244}e^{6} - \frac{588943}{204244}e^{5} + \frac{1490225}{102122}e^{4} + \frac{314568}{51061}e^{3} - \frac{1275817}{51061}e^{2} - \frac{504}{51061}e + \frac{424760}{51061}$ |
| 31 | $[31, 31, -w - 4]$ | $...$ |
| 31 | $[31, 31, w - 5]$ | $...$ |
| 41 | $[41, 41, 3w - 22]$ | $\phantom{-}\frac{501}{51061}e^{10} + \frac{1298}{51061}e^{9} - \frac{6613}{51061}e^{8} - \frac{21143}{51061}e^{7} + \frac{1383}{51061}e^{6} + \frac{90947}{51061}e^{5} + \frac{239179}{51061}e^{4} - \frac{17996}{51061}e^{3} - \frac{717528}{51061}e^{2} - \frac{209264}{51061}e + \frac{293374}{51061}$ |
| 47 | $[47, 47, w + 19]$ | $...$ |
| 47 | $[47, 47, w + 27]$ | $...$ |
| 53 | $[53, 53, w + 14]$ | $...$ |
| 53 | $[53, 53, w + 38]$ | $...$ |
| 59 | $[59, 59, -w - 10]$ | $...$ |
| 59 | $[59, 59, w - 11]$ | $...$ |
| 61 | $[61, 61, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 3]$ | $1$ |
| $5$ | $[5,5,w + 7]$ | $1$ |