Base field 5.5.170701.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[28, 14, w^{4} - 2w^{3} - 5w^{2} + 4w + 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $29$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 3x^{6} - 27x^{5} + 97x^{4} + 107x^{3} - 593x^{2} + 335x + 211\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $-1$ |
| 8 | $[8, 2, -2w^{4} + 3w^{3} + 10w^{2} - 5w - 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{4} - w^{3} - 6w^{2} + 2]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{27}{16}e^{4} + e^{3} + \frac{163}{16}e^{2} - 7e - \frac{105}{16}$ |
| 13 | $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ | $-\frac{1}{16}e^{6} + \frac{27}{16}e^{4} - e^{3} - \frac{163}{16}e^{2} + 7e + \frac{137}{16}$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{1}{8}e^{6} + \frac{1}{8}e^{5} - 3e^{4} - \frac{1}{4}e^{3} + \frac{125}{8}e^{2} - \frac{55}{8}e - \frac{39}{4}$ |
| 23 | $[23, 23, -w + 2]$ | $-\frac{3}{16}e^{6} + \frac{1}{8}e^{5} + \frac{83}{16}e^{4} - \frac{25}{4}e^{3} - \frac{493}{16}e^{2} + \frac{313}{8}e + \frac{205}{16}$ |
| 31 | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $-\frac{1}{8}e^{6} + \frac{27}{8}e^{4} - \frac{5}{2}e^{3} - \frac{167}{8}e^{2} + \frac{41}{2}e + \frac{125}{8}$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{4}e^{5} - \frac{35}{16}e^{4} + \frac{13}{2}e^{3} + \frac{243}{16}e^{2} - \frac{129}{4}e - \frac{113}{16}$ |
| 47 | $[47, 47, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{13}{2}e^{4} + 5e^{3} + \frac{145}{4}e^{2} - 39e - 12$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{8}e^{5} - \frac{15}{4}e^{4} + \frac{19}{4}e^{3} + \frac{205}{8}e^{2} - \frac{205}{8}e - 23$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 4w - 3]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{13}{2}e^{4} + 5e^{3} + \frac{145}{4}e^{2} - 41e - 12$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{25}{8}e^{4} + 3e^{3} + \frac{135}{8}e^{2} - 25e - \frac{79}{8}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 7w^{2} + 3w + 6]$ | $-e^{2} + 9$ |
| 71 | $[71, 71, -2w^{4} + 2w^{3} + 11w^{2} - 2]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - 5e^{3} - \frac{9}{2}e^{2} + \frac{75}{4}e - 2$ |
| 71 | $[71, 71, -w^{4} + 3w^{3} + 3w^{2} - 9w - 1]$ | $-\frac{5}{16}e^{6} + \frac{135}{16}e^{4} - 6e^{3} - \frac{831}{16}e^{2} + 50e + \frac{637}{16}$ |
| 73 | $[73, 73, 2w^{4} - 4w^{3} - 9w^{2} + 10w + 5]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{4}e^{5} - \frac{35}{16}e^{4} + \frac{13}{2}e^{3} + \frac{259}{16}e^{2} - \frac{121}{4}e - \frac{193}{16}$ |
| 79 | $[79, 79, 2w^{4} - 3w^{3} - 11w^{2} + 4w + 8]$ | $-\frac{1}{4}e^{6} + \frac{13}{2}e^{4} - 5e^{3} - \frac{149}{4}e^{2} + 39e + 21$ |
| 83 | $[83, 83, -3w^{4} + 5w^{3} + 15w^{2} - 9w - 10]$ | $\phantom{-}\frac{1}{8}e^{6} + \frac{1}{8}e^{5} - \frac{13}{4}e^{4} - \frac{3}{4}e^{3} + \frac{157}{8}e^{2} - \frac{35}{8}e - \frac{23}{2}$ |
| 89 | $[89, 89, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}e^{2} - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $-1$ |
| $7$ | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $1$ |