Base field 5.5.65657.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 3x^{4} - 13x^{3} - 23x^{2} + 28x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $-1$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ | $\phantom{-}\frac{7}{19}e^{4} + \frac{22}{19}e^{3} - \frac{96}{19}e^{2} - \frac{191}{19}e + \frac{166}{19}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $-\frac{7}{19}e^{4} - \frac{22}{19}e^{3} + \frac{96}{19}e^{2} + \frac{191}{19}e - \frac{147}{19}$ |
| 29 | $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ | $-\frac{4}{19}e^{4} - \frac{18}{19}e^{3} + \frac{44}{19}e^{2} + \frac{139}{19}e - \frac{141}{19}$ |
| 32 | $[32, 2, 2]$ | $-\frac{4}{19}e^{4} - \frac{18}{19}e^{3} + \frac{25}{19}e^{2} + \frac{158}{19}e + \frac{30}{19}$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{11}{19}e^{4} - \frac{40}{19}e^{3} + \frac{121}{19}e^{2} + \frac{311}{19}e - \frac{212}{19}$ |
| 41 | $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ | $\phantom{-}\frac{11}{19}e^{4} + \frac{40}{19}e^{3} - \frac{102}{19}e^{2} - \frac{292}{19}e + \frac{60}{19}$ |
| 43 | $[43, 43, -2w^{4} + 3w^{3} + 8w^{2} - 8w - 6]$ | $-\frac{6}{19}e^{4} - \frac{8}{19}e^{3} + \frac{85}{19}e^{2} + \frac{28}{19}e - \frac{164}{19}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 5w^{2} + 6w + 5]$ | $-\frac{2}{19}e^{4} - \frac{9}{19}e^{3} + \frac{22}{19}e^{2} + \frac{41}{19}e - \frac{42}{19}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ | $-1$ |
| 61 | $[61, 61, w^{2} - 2w - 3]$ | $\phantom{-}e^{4} + 3e^{3} - 12e^{2} - 22e + 13$ |
| 67 | $[67, 67, w^{4} - w^{3} - 4w^{2} + 3w]$ | $\phantom{-}\frac{14}{19}e^{4} + \frac{44}{19}e^{3} - \frac{173}{19}e^{2} - \frac{344}{19}e + \frac{142}{19}$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $-\frac{1}{19}e^{4} - \frac{14}{19}e^{3} - \frac{8}{19}e^{2} + \frac{125}{19}e - \frac{59}{19}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 5]$ | $\phantom{-}\frac{1}{19}e^{4} + \frac{14}{19}e^{3} - \frac{11}{19}e^{2} - \frac{144}{19}e + \frac{135}{19}$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 5w + 3]$ | $\phantom{-}\frac{5}{19}e^{4} + \frac{13}{19}e^{3} - \frac{74}{19}e^{2} - \frac{150}{19}e + \frac{162}{19}$ |
| 71 | $[71, 71, 2w^{4} - 2w^{3} - 8w^{2} + 5w + 4]$ | $-\frac{14}{19}e^{4} - \frac{44}{19}e^{3} + \frac{173}{19}e^{2} + \frac{325}{19}e - \frac{351}{19}$ |
| 73 | $[73, 73, -2w^{4} + 2w^{3} + 9w^{2} - 5w - 6]$ | $\phantom{-}\frac{10}{19}e^{4} + \frac{26}{19}e^{3} - \frac{110}{19}e^{2} - \frac{129}{19}e + \frac{134}{19}$ |
| 81 | $[81, 3, -2w^{4} + 3w^{3} + 10w^{2} - 9w - 10]$ | $-\frac{5}{19}e^{4} - \frac{13}{19}e^{3} + \frac{55}{19}e^{2} - \frac{2}{19}e - \frac{67}{19}$ |
| 97 | $[97, 97, -2w^{4} + 3w^{3} + 7w^{2} - 5w - 4]$ | $\phantom{-}\frac{18}{19}e^{4} + \frac{62}{19}e^{3} - \frac{217}{19}e^{2} - \frac{559}{19}e + \frac{226}{19}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ | $1$ |