Base field 3.3.1257.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 9\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[15, 15, w + 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - x^{6} - 18x^{5} + 15x^{4} + 88x^{3} - 24x^{2} - 144x - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 3]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 2]$ | $-1$ |
| 5 | $[5, 5, w^{2} + w - 5]$ | $\phantom{-}1$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{4}e^{5} - 4e^{4} - \frac{13}{4}e^{3} + \frac{29}{2}e^{2} + 11e - 3$ |
| 13 | $[13, 13, w + 2]$ | $-\frac{1}{4}e^{6} + \frac{15}{4}e^{4} - \frac{1}{4}e^{3} - \frac{47}{4}e^{2} - 3e + 6$ |
| 13 | $[13, 13, -2w + 5]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 8e^{4} - \frac{15}{2}e^{3} - 28e^{2} + 14e + 22$ |
| 13 | $[13, 13, -w^{2} - w + 4]$ | $-\frac{1}{4}e^{6} + \frac{15}{4}e^{4} - \frac{1}{4}e^{3} - \frac{43}{4}e^{2} - 3e - 2$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{7}{2}e^{3} + \frac{15}{4}e^{2} + 7e - 4$ |
| 23 | $[23, 23, -w^{2} - w + 7]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 8e^{4} - \frac{17}{2}e^{3} - 30e^{2} + 24e + 32$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - 8e^{3} - \frac{13}{2}e^{2} + 27e + 22$ |
| 29 | $[29, 29, w^{2} - 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{5}{4}e^{5} - \frac{33}{4}e^{4} + 19e^{3} + \frac{131}{4}e^{2} - 49e - 50$ |
| 31 | $[31, 31, w^{2} + w - 8]$ | $\phantom{-}\frac{3}{2}e^{5} + \frac{1}{2}e^{4} - 23e^{3} - \frac{15}{2}e^{2} + 70e + 48$ |
| 41 | $[41, 41, w^{2} + w - 11]$ | $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{7}{2}e^{3} + \frac{33}{4}e^{2} - 11e - 14$ |
| 47 | $[47, 47, w^{2} + 2w - 1]$ | $-\frac{1}{2}e^{6} + \frac{1}{4}e^{5} + \frac{33}{4}e^{4} - 4e^{3} - \frac{127}{4}e^{2} + 9e + 24$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{3}{2}e^{5} - \frac{17}{4}e^{4} + \frac{93}{4}e^{3} + \frac{77}{4}e^{2} - 69e - 52$ |
| 61 | $[61, 61, -w^{2} + 5w - 7]$ | $-\frac{1}{2}e^{6} + e^{5} + \frac{17}{2}e^{4} - \frac{33}{2}e^{3} - \frac{73}{2}e^{2} + 52e + 54$ |
| 67 | $[67, 67, 2w^{2} - 13]$ | $-e^{5} - e^{4} + 16e^{3} + 15e^{2} - 54e - 52$ |
| 89 | $[89, 89, -2w^{2} + w + 20]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - 8e^{3} - \frac{17}{2}e^{2} + 28e + 34$ |
| 89 | $[89, 89, 5w^{2} + 8w - 19]$ | $\phantom{-}e^{5} + e^{4} - 16e^{3} - 12e^{2} + 56e + 42$ |
| 89 | $[89, 89, w^{2} + 2w - 7]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{15}{2}e^{4} + \frac{1}{2}e^{3} + \frac{47}{2}e^{2} + 4e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 2]$ | $1$ |
| $5$ | $[5, 5, w^{2} + w - 5]$ | $-1$ |