Base field 3.3.1101.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[12, 6, w^{2} + w - 5]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 2x^{6} - 11x^{5} + 20x^{4} + 32x^{3} - 45x^{2} - 32x + 21\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 3]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 5e^{4} + 4e^{3} + 10e^{2} - \frac{7}{2}e - \frac{3}{2}$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}1$ |
| 4 | $[4, 2, w^{2} + w - 7]$ | $-1$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 5e^{4} + 3e^{3} + 9e^{2} + \frac{5}{2}e + \frac{5}{2}$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 4e^{4} - 3e^{3} - 3e^{2} - \frac{3}{2}e - \frac{9}{2}$ |
| 31 | $[31, 31, -2w^{2} + 19]$ | $-e^{5} + e^{4} + 10e^{3} - 8e^{2} - 17e + 7$ |
| 31 | $[31, 31, -w^{2} + 5]$ | $-e^{5} + 2e^{4} + 9e^{3} - 17e^{2} - 12e + 19$ |
| 31 | $[31, 31, -3w + 5]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - 7e^{4} - 15e^{3} + 25e^{2} + \frac{61}{2}e - \frac{23}{2}$ |
| 41 | $[41, 41, w^{2} + 2w - 7]$ | $-e^{5} + 2e^{4} + 9e^{3} - 17e^{2} - 16e + 21$ |
| 43 | $[43, 43, w^{2} - 11]$ | $-e^{5} + 2e^{4} + 9e^{3} - 15e^{2} - 12e + 13$ |
| 47 | $[47, 47, 3w - 7]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - 8e^{4} - 15e^{3} + 35e^{2} + \frac{55}{2}e - \frac{51}{2}$ |
| 53 | $[53, 53, -3w^{2} - 6w + 11]$ | $\phantom{-}e^{6} - e^{5} - 10e^{4} + 8e^{3} + 22e^{2} - 7e - 15$ |
| 59 | $[59, 59, 2w - 1]$ | $\phantom{-}e^{6} - 3e^{5} - 8e^{4} + 26e^{3} + 4e^{2} - 33e + 9$ |
| 67 | $[67, 67, 2w^{2} + w - 19]$ | $-\frac{1}{2}e^{6} + \frac{5}{2}e^{5} + e^{4} - 23e^{3} + 21e^{2} + \frac{75}{2}e - \frac{53}{2}$ |
| 67 | $[67, 67, 3w^{2} + 2w - 25]$ | $\phantom{-}e^{5} - e^{4} - 8e^{3} + 8e^{2} + 7e - 11$ |
| 67 | $[67, 67, w - 5]$ | $-2e^{6} + e^{5} + 21e^{4} - 4e^{3} - 50e^{2} - 13e + 19$ |
| 73 | $[73, 73, -4w^{2} - 3w + 29]$ | $\phantom{-}\frac{3}{2}e^{6} - \frac{1}{2}e^{5} - 17e^{4} + 2e^{3} + 48e^{2} + \frac{7}{2}e - \frac{55}{2}$ |
| 73 | $[73, 73, 2w^{2} - w - 11]$ | $-e^{6} - e^{5} + 12e^{4} + 10e^{3} - 34e^{2} - 19e + 7$ |
| 73 | $[73, 73, w^{2} + 2w - 11]$ | $-2e^{6} + 2e^{5} + 20e^{4} - 16e^{3} - 42e^{2} + 14e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $-1$ |
| $4$ | $[4, 2, w^{2} + w - 7]$ | $1$ |