Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -w + 2]$ |
| 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:
| \(x^{7} + 3x^{6} - 14x^{5} - 27x^{4} + 84x^{3} + 39x^{2} - 185x + 98\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e^{6} + \frac{9}{2}e^{5} - 7e^{4} - \frac{75}{2}e^{3} + 25e^{2} + \frac{157}{2}e - 61$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{1}{2}e^{6} + 2e^{5} - \frac{9}{2}e^{4} - 18e^{3} + \frac{35}{2}e^{2} + 41e - 36$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w + 1]$ | $-\frac{3}{2}e^{6} - \frac{13}{2}e^{5} + \frac{23}{2}e^{4} + \frac{109}{2}e^{3} - \frac{89}{2}e^{2} - \frac{229}{2}e + 101$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{6} + \frac{9}{2}e^{5} - 7e^{4} - \frac{75}{2}e^{3} + 24e^{2} + \frac{153}{2}e - 56$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}4e^{6} + 18e^{5} - 30e^{4} - 154e^{3} + 117e^{2} + 332e - 278$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}2e^{6} + 9e^{5} - 15e^{4} - 77e^{3} + 60e^{2} + 168e - 146$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-\frac{1}{2}e^{5} - 2e^{4} + \frac{5}{2}e^{3} + 12e^{2} - \frac{7}{2}e - 13$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{5}{2}e^{5} - \frac{7}{2}e^{4} - \frac{45}{2}e^{3} + \frac{31}{2}e^{2} + \frac{107}{2}e - 45$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-e^{6} - 4e^{5} + 10e^{4} + 38e^{3} - 44e^{2} - 89e + 90$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $-e^{4} - 3e^{3} + 7e^{2} + 14e - 16$ |
| 37 | $[37, 37, -w - 4]$ | $-5e^{6} - 22e^{5} + 39e^{4} + 189e^{3} - 152e^{2} - 404e + 344$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-\frac{1}{2}e^{6} - \frac{3}{2}e^{5} + \frac{15}{2}e^{4} + \frac{35}{2}e^{3} - \frac{75}{2}e^{2} - \frac{89}{2}e + 61$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{7}{2}e^{6} - 15e^{5} + \frac{55}{2}e^{4} + 128e^{3} - \frac{211}{2}e^{2} - 275e + 240$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $-\frac{11}{2}e^{6} - \frac{49}{2}e^{5} + \frac{83}{2}e^{4} + \frac{419}{2}e^{3} - \frac{315}{2}e^{2} - \frac{897}{2}e + 367$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-5e^{6} - \frac{45}{2}e^{5} + 37e^{4} + \frac{383}{2}e^{3} - 142e^{2} - \frac{825}{2}e + 339$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $\phantom{-}\frac{3}{2}e^{6} + \frac{13}{2}e^{5} - \frac{21}{2}e^{4} - \frac{103}{2}e^{3} + \frac{75}{2}e^{2} + \frac{205}{2}e - 81$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $\phantom{-}e^{6} + \frac{7}{2}e^{5} - 9e^{4} - \frac{55}{2}e^{3} + 33e^{2} + \frac{101}{2}e - 49$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $-\frac{1}{2}e^{6} - 3e^{5} + \frac{3}{2}e^{4} + 24e^{3} - \frac{9}{2}e^{2} - 49e + 38$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w + 2]$ | $-1$ |