Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[4, 2, w^{2} + w + 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 4x^{6} - 2x^{5} - 20x^{4} - 7x^{3} + 19x^{2} + 2x - 1\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $-1$ |
| 5 | $[5, 5, w]$ | $-\frac{1}{2}e^{6} - \frac{1}{2}e^{5} + \frac{7}{2}e^{4} + \frac{1}{2}e^{3} - 6e^{2} + \frac{11}{2}e - \frac{3}{2}$ |
| 11 | $[11, 11, 10w + 4]$ | $-e^{6} - 3e^{5} + 4e^{4} + 14e^{3} - e^{2} - 9e - 2$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $\phantom{-}e^{6} + 2e^{5} - 6e^{4} - 9e^{3} + 9e^{2} + 5e - 2$ |
| 17 | $[17, 17, w + 1]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - \frac{3}{2}e^{4} - \frac{9}{2}e^{3} - e^{2} - \frac{7}{2}e + \frac{7}{2}$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $-e^{4} - e^{3} + 5e^{2} + 2e - 3$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $-\frac{1}{2}e^{6} - \frac{7}{2}e^{5} - \frac{5}{2}e^{4} + \frac{33}{2}e^{3} + 16e^{2} - \frac{27}{2}e - \frac{3}{2}$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $-e^{6} - 3e^{5} + 4e^{4} + 15e^{3} - 2e^{2} - 17e + 2$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $\phantom{-}2e^{6} + 7e^{5} - 6e^{4} - 33e^{3} - 5e^{2} + 24e + 1$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $\phantom{-}\frac{5}{2}e^{6} + \frac{15}{2}e^{5} - \frac{17}{2}e^{4} - \frac{65}{2}e^{3} - 2e^{2} + \frac{35}{2}e - \frac{3}{2}$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}e^{6} + 4e^{5} - 3e^{4} - 22e^{3} - 3e^{2} + 26e - 1$ |
| 29 | $[29, 29, w + 7]$ | $\phantom{-}\frac{3}{2}e^{6} + \frac{9}{2}e^{5} - \frac{11}{2}e^{4} - \frac{43}{2}e^{3} - 3e^{2} + \frac{33}{2}e + \frac{5}{2}$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $\phantom{-}e^{5} + 3e^{4} - 5e^{3} - 11e^{2} + 8e - 2$ |
| 43 | $[43, 43, w^{2} - 11]$ | $-4e^{6} - 13e^{5} + 14e^{4} + 61e^{3} + 3e^{2} - 44e - 1$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $-2e^{6} - 4e^{5} + 14e^{4} + 20e^{3} - 27e^{2} - 15e + 8$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-e^{6} - 6e^{5} - 2e^{4} + 29e^{3} + 20e^{2} - 23e + 1$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + \frac{9}{2}e^{4} - \frac{15}{2}e^{3} - 8e^{2} + \frac{49}{2}e - \frac{9}{2}$ |
| 79 | $[79, 79, w^{2} + 37]$ | $-3e^{5} - 5e^{4} + 21e^{3} + 21e^{2} - 36e - 4$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - \frac{1}{2}e^{4} - \frac{7}{2}e^{3} - 6e^{2} - \frac{23}{2}e - \frac{3}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{2} + w + 1]$ | $1$ |