Base field 3.3.1373.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[4, 2, w^{2} - w - 7]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 2x^{6} - 10x^{5} + 16x^{4} + 31x^{3} - 32x^{2} - 28x + 8\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{1}{4}e^{6} + \frac{1}{2}e^{5} + 2e^{4} - \frac{7}{2}e^{3} - \frac{17}{4}e^{2} + \frac{11}{2}e + 2$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w]$ | $-\frac{1}{2}e^{5} + e^{4} + 3e^{3} - 5e^{2} - \frac{7}{2}e + 4$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{9}{2}e^{3} - \frac{5}{2}e^{2} - 9e + 2$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{1}{2}e^{5} - \frac{3}{2}e^{4} + 2e^{3} + \frac{11}{4}e^{2} - 4$ |
| 25 | $[25, 5, w^{2} - 8]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - \frac{11}{2}e^{4} + \frac{7}{2}e^{3} + 15e^{2} - 5e - 3$ |
| 29 | $[29, 29, 2w + 3]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - \frac{7}{2}e^{4} + \frac{3}{2}e^{3} + 4e^{2} + e + 8$ |
| 37 | $[37, 37, w + 4]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - \frac{11}{2}e^{4} + \frac{9}{2}e^{3} + 16e^{2} - 12e - 6$ |
| 37 | $[37, 37, -3w^{2} + 2w + 24]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - \frac{11}{2}e^{4} + \frac{7}{2}e^{3} + 16e^{2} - 3e - 6$ |
| 37 | $[37, 37, w^{2} + 2w - 2]$ | $\phantom{-}\frac{3}{4}e^{6} - 2e^{5} - \frac{11}{2}e^{4} + 12e^{3} + \frac{49}{4}e^{2} - \frac{25}{2}e - 8$ |
| 47 | $[47, 47, w^{2} - 2]$ | $-\frac{1}{4}e^{6} + 3e^{4} + \frac{3}{2}e^{3} - \frac{41}{4}e^{2} - 8e + 12$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $-\frac{1}{4}e^{6} + \frac{3}{2}e^{5} - \frac{21}{2}e^{3} + \frac{23}{4}e^{2} + \frac{35}{2}e$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}e^{5} - 2e^{4} - 7e^{3} + 8e^{2} + 10e$ |
| 71 | $[71, 71, 2w - 1]$ | $\phantom{-}\frac{1}{4}e^{6} + e^{5} - 3e^{4} - \frac{19}{2}e^{3} + \frac{25}{4}e^{2} + 23e + 4$ |
| 71 | $[71, 71, -w^{2} + 4w + 2]$ | $-e^{4} + 3e^{3} + 5e^{2} - 11e - 8$ |
| 71 | $[71, 71, -w^{2} + 4w - 2]$ | $-e^{6} + e^{5} + \frac{19}{2}e^{4} - \frac{13}{2}e^{3} - \frac{49}{2}e^{2} + \frac{23}{2}e + 14$ |
| 73 | $[73, 73, -w^{2} + 4w + 4]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{3}{2}e^{5} - \frac{7}{2}e^{4} - 13e^{3} + \frac{35}{4}e^{2} + 27e + 2$ |
| 79 | $[79, 79, -2w + 7]$ | $-\frac{1}{2}e^{6} + e^{5} + 6e^{4} - 9e^{3} - \frac{37}{2}e^{2} + 17e + 6$ |
| 83 | $[83, 83, -2w^{2} + 13]$ | $-e^{4} + 7e^{2} + 2e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{2} - w - 7]$ | $-1$ |