Base field 3.3.1944.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 6\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w^{2} - w - 7]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} - 4x^{14} - 16x^{13} + 82x^{12} + 58x^{11} - 612x^{10} + 269x^{9} + 1904x^{8} - 2161x^{7} - 1655x^{6} + 3739x^{5} - 1621x^{4} - 144x^{3} + 176x^{2} - 4x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2w + 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 3 | $[3, 3, w^{2} - w - 9]$ | $...$ |
| 7 | $[7, 7, w^{2} - w - 7]$ | $-1$ |
| 11 | $[11, 11, w^{2} - w - 1]$ | $...$ |
| 13 | $[13, 13, -2w - 1]$ | $...$ |
| 17 | $[17, 17, -2w^{2} + 6w + 5]$ | $...$ |
| 31 | $[31, 31, -2w^{2} + 2w + 19]$ | $-\frac{11}{4}e^{14} + \frac{37}{4}e^{13} + 50e^{12} - \frac{389}{2}e^{11} - \frac{567}{2}e^{10} + 1515e^{9} + \frac{835}{4}e^{8} - \frac{20657}{4}e^{7} + \frac{11109}{4}e^{6} + \frac{12821}{2}e^{5} - 6493e^{4} + \frac{723}{2}e^{3} + \frac{3181}{4}e^{2} - 16e - \frac{47}{2}$ |
| 37 | $[37, 37, 2w^{2} - 13]$ | $...$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $...$ |
| 43 | $[43, 43, 2w^{2} - 2w - 17]$ | $...$ |
| 43 | $[43, 43, -2w + 7]$ | $...$ |
| 43 | $[43, 43, 12w^{2} - 8w - 101]$ | $...$ |
| 49 | $[49, 7, w^{2} + w - 1]$ | $...$ |
| 59 | $[59, 59, -w^{2} + w + 11]$ | $...$ |
| 61 | $[61, 61, -w^{2} - w - 1]$ | $...$ |
| 79 | $[79, 79, -2w^{2} + 4w + 7]$ | $...$ |
| 83 | $[83, 83, 2w - 1]$ | $...$ |
| 89 | $[89, 89, 5w^{2} - 3w - 43]$ | $...$ |
| 103 | $[103, 103, -2w + 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w^{2} - w - 7]$ | $1$ |