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: | $[5, 5, w]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 12x^{6} + 42x^{4} + 5x^{3} - 45x^{2} - 11x + 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{2}{13}e^{7} + \frac{3}{13}e^{6} + 2e^{5} - 2e^{4} - \frac{97}{13}e^{3} + \frac{38}{13}e^{2} + \frac{111}{13}e + \frac{5}{13}$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $-\frac{5}{13}e^{7} + \frac{1}{13}e^{6} + 4e^{5} - e^{4} - \frac{132}{13}e^{3} + \frac{17}{13}e^{2} + \frac{63}{13}e + \frac{6}{13}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $-\frac{1}{13}e^{7} - \frac{5}{13}e^{6} + e^{5} + 4e^{4} - \frac{55}{13}e^{3} - \frac{137}{13}e^{2} + \frac{49}{13}e + \frac{74}{13}$ |
| 13 | $[13, 13, -w + 2]$ | $-\frac{4}{13}e^{7} + \frac{6}{13}e^{6} + 4e^{5} - 5e^{4} - \frac{194}{13}e^{3} + \frac{167}{13}e^{2} + \frac{196}{13}e - \frac{42}{13}$ |
| 25 | $[25, 5, w^{2} - 8]$ | $-\frac{7}{13}e^{7} + \frac{4}{13}e^{6} + 6e^{5} - 4e^{4} - \frac{229}{13}e^{3} + \frac{172}{13}e^{2} + \frac{148}{13}e - \frac{132}{13}$ |
| 29 | $[29, 29, 2w + 3]$ | $\phantom{-}\frac{7}{13}e^{7} - \frac{4}{13}e^{6} - 6e^{5} + 3e^{4} + \frac{229}{13}e^{3} - \frac{42}{13}e^{2} - \frac{174}{13}e - \frac{63}{13}$ |
| 37 | $[37, 37, w + 4]$ | $\phantom{-}\frac{9}{13}e^{7} - \frac{7}{13}e^{6} - 8e^{5} + 5e^{4} + \frac{313}{13}e^{3} - \frac{119}{13}e^{2} - \frac{194}{13}e + \frac{75}{13}$ |
| 37 | $[37, 37, -3w^{2} + 2w + 24]$ | $-\frac{3}{13}e^{7} + \frac{11}{13}e^{6} + 2e^{5} - 8e^{4} - \frac{22}{13}e^{3} + \frac{200}{13}e^{2} - \frac{61}{13}e - \frac{51}{13}$ |
| 37 | $[37, 37, w^{2} + 2w - 2]$ | $-\frac{12}{13}e^{7} + \frac{5}{13}e^{6} + 9e^{5} - 5e^{4} - \frac{270}{13}e^{3} + \frac{150}{13}e^{2} + \frac{133}{13}e - \frac{74}{13}$ |
| 47 | $[47, 47, w^{2} - 2]$ | $-\frac{1}{13}e^{7} - \frac{5}{13}e^{6} + e^{5} + 3e^{4} - \frac{42}{13}e^{3} - \frac{20}{13}e^{2} + \frac{10}{13}e - \frac{108}{13}$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}\frac{2}{13}e^{7} + \frac{10}{13}e^{6} - 2e^{5} - 7e^{4} + \frac{123}{13}e^{3} + \frac{183}{13}e^{2} - \frac{163}{13}e - \frac{18}{13}$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}\frac{17}{13}e^{7} - \frac{6}{13}e^{6} - 15e^{5} + 5e^{4} + \frac{597}{13}e^{3} - \frac{89}{13}e^{2} - \frac{417}{13}e - \frac{36}{13}$ |
| 71 | $[71, 71, 2w - 1]$ | $\phantom{-}\frac{1}{13}e^{7} + \frac{5}{13}e^{6} - 5e^{4} - \frac{75}{13}e^{3} + \frac{241}{13}e^{2} + \frac{198}{13}e - \frac{165}{13}$ |
| 71 | $[71, 71, -w^{2} + 4w + 2]$ | $-\frac{19}{13}e^{7} + \frac{9}{13}e^{6} + 16e^{5} - 8e^{4} - \frac{590}{13}e^{3} + \frac{231}{13}e^{2} + \frac{385}{13}e - \frac{24}{13}$ |
| 71 | $[71, 71, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{7}{13}e^{7} - \frac{4}{13}e^{6} - 7e^{5} + 3e^{4} + \frac{359}{13}e^{3} - \frac{81}{13}e^{2} - \frac{447}{13}e - \frac{24}{13}$ |
| 73 | $[73, 73, -w^{2} + 4w + 4]$ | $-e^{6} + 11e^{4} - 30e^{2} - 2e + 18$ |
| 79 | $[79, 79, -2w + 7]$ | $\phantom{-}\frac{2}{13}e^{7} - \frac{16}{13}e^{6} - 2e^{5} + 12e^{4} + \frac{71}{13}e^{3} - \frac{350}{13}e^{2} - \frac{33}{13}e + \frac{216}{13}$ |
| 83 | $[83, 83, -2w^{2} + 13]$ | $-\frac{7}{13}e^{7} + \frac{17}{13}e^{6} + 5e^{5} - 12e^{4} - \frac{99}{13}e^{3} + \frac{263}{13}e^{2} - \frac{73}{13}e - \frac{54}{13}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $-1$ |