Base field 3.3.1300.1
Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w + 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + x^{6} - 10x^{5} - 7x^{4} + 27x^{3} + 12x^{2} - 18x - 8\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + 2w + 5]$ | $-\frac{1}{2}e^{6} - \frac{1}{2}e^{5} + 5e^{4} + \frac{5}{2}e^{3} - \frac{27}{2}e^{2} + 7$ |
| 7 | $[7, 7, w + 3]$ | $-1$ |
| 11 | $[11, 11, -2w^{2} + 5w + 9]$ | $\phantom{-}e^{2} + e - 4$ |
| 13 | $[13, 13, -w^{2} + w + 7]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - 5e^{4} - \frac{5}{2}e^{3} + \frac{25}{2}e^{2} - e - 5$ |
| 13 | $[13, 13, w - 3]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 6e^{4} + \frac{9}{2}e^{3} + \frac{37}{2}e^{2} - 8e - 13$ |
| 17 | $[17, 17, -w^{2} + 2w + 7]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - 3e^{4} - \frac{23}{2}e^{3} - \frac{1}{2}e^{2} + 16e + 7$ |
| 17 | $[17, 17, -2w^{2} + 5w + 7]$ | $-e^{5} - 2e^{4} + 8e^{3} + 12e^{2} - 13e - 10$ |
| 17 | $[17, 17, -w^{2} + 3w + 3]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 6e^{4} - \frac{9}{2}e^{3} - \frac{37}{2}e^{2} + 8e + 11$ |
| 19 | $[19, 19, -w + 1]$ | $\phantom{-}2e^{6} + 2e^{5} - 18e^{4} - 11e^{3} + 39e^{2} + 6e - 14$ |
| 27 | $[27, 3, -3]$ | $-e^{6} - 2e^{5} + 8e^{4} + 13e^{3} - 15e^{2} - 13e + 4$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $-e^{6} + 10e^{4} - 2e^{3} - 25e^{2} + 6e + 10$ |
| 37 | $[37, 37, w^{2} - 7]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 6e^{4} + \frac{11}{2}e^{3} + \frac{41}{2}e^{2} - 11e - 17$ |
| 41 | $[41, 41, w^{2} - w - 11]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 6e^{4} - \frac{11}{2}e^{3} - \frac{41}{2}e^{2} + 13e + 17$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-e^{6} - e^{5} + 9e^{4} + 6e^{3} - 18e^{2} - 5e - 2$ |
| 49 | $[49, 7, w^{2} - 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - 4e^{4} - \frac{5}{2}e^{3} + \frac{15}{2}e^{2} - e - 7$ |
| 59 | $[59, 59, w^{2} - 4w + 1]$ | $-e^{6} + e^{5} + 11e^{4} - 10e^{3} - 31e^{2} + 20e + 20$ |
| 67 | $[67, 67, w^{2} - 3w - 7]$ | $\phantom{-}e^{6} - 10e^{4} + 5e^{3} + 26e^{2} - 20e - 16$ |
| 71 | $[71, 71, 4w + 9]$ | $-e^{6} - e^{5} + 10e^{4} + 6e^{3} - 26e^{2} - 4e + 12$ |
| 73 | $[73, 73, -4w^{2} + 8w + 23]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 7e^{4} + \frac{9}{2}e^{3} + \frac{51}{2}e^{2} - 8e - 25$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 3]$ | $1$ |