Base field 5.5.65657.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[53, 53, -w^{4} + w^{3} + 4 w^{2} - w - 4]$ |
| 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:
| \(x^{5} + 3 x^{4} - 13 x^{3} - 23 x^{2} + 28 x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{4} + w^{3} + 4 w^{2} - 2 w - 2]$ | $-1$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 19 | $[19, 19, w^{4} - 2 w^{3} - 4 w^{2} + 5 w + 4]$ | $\phantom{-}\frac{7}{19} e^{4} + \frac{22}{19} e^{3} - \frac{96}{19} e^{2} - \frac{191}{19} e + \frac{166}{19}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3 w - 1]$ | $-\frac{7}{19} e^{4} - \frac{22}{19} e^{3} + \frac{96}{19} e^{2} + \frac{191}{19} e - \frac{147}{19}$ |
| 29 | $[29, 29, 2 w^{4} - 3 w^{3} - 8 w^{2} + 7 w + 4]$ | $-\frac{4}{19} e^{4} - \frac{18}{19} e^{3} + \frac{44}{19} e^{2} + \frac{139}{19} e - \frac{141}{19}$ |
| 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 | $[37, 37, w^{3} - 2 w^{2} - 2 w + 2]$ | $-\frac{11}{19} e^{4} - \frac{40}{19} e^{3} + \frac{121}{19} e^{2} + \frac{311}{19} e - \frac{212}{19}$ |
| 41 | $[41, 41, -2 w^{4} + 3 w^{3} + 9 w^{2} - 8 w - 6]$ | $\phantom{-}\frac{11}{19} e^{4} + \frac{40}{19} e^{3} - \frac{102}{19} e^{2} - \frac{292}{19} e + \frac{60}{19}$ |
| 43 | $[43, 43, -2 w^{4} + 3 w^{3} + 8 w^{2} - 8 w - 6]$ | $-\frac{6}{19} e^{4} - \frac{8}{19} e^{3} + \frac{85}{19} e^{2} + \frac{28}{19} e - \frac{164}{19}$ |
| 47 | $[47, 47, w^{4} - 2 w^{3} - 5 w^{2} + 6 w + 5]$ | $-\frac{2}{19} e^{4} - \frac{9}{19} e^{3} + \frac{22}{19} e^{2} + \frac{41}{19} e - \frac{42}{19}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4 w^{2} - w - 4]$ | $-1$ |
| 61 | $[61, 61, w^{2} - 2 w - 3]$ | $\phantom{-}e^{4} + 3 e^{3} - 12 e^{2} - 22 e + 13$ |
| 67 | $[67, 67, w^{4} - w^{3} - 4 w^{2} + 3 w]$ | $\phantom{-}\frac{14}{19} e^{4} + \frac{44}{19} e^{3} - \frac{173}{19} e^{2} - \frac{344}{19} e + \frac{142}{19}$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5 w^{2} - 2 w - 2]$ | $-\frac{1}{19} e^{4} - \frac{14}{19} e^{3} - \frac{8}{19} e^{2} + \frac{125}{19} e - \frac{59}{19}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4 w^{2} + 5]$ | $\phantom{-}\frac{1}{19} e^{4} + \frac{14}{19} e^{3} - \frac{11}{19} e^{2} - \frac{144}{19} e + \frac{135}{19}$ |
| 71 | $[71, 71, w^{4} - 2 w^{3} - 3 w^{2} + 5 w + 3]$ | $\phantom{-}\frac{5}{19} e^{4} + \frac{13}{19} e^{3} - \frac{74}{19} e^{2} - \frac{150}{19} e + \frac{162}{19}$ |
| 71 | $[71, 71, 2 w^{4} - 2 w^{3} - 8 w^{2} + 5 w + 4]$ | $-\frac{14}{19} e^{4} - \frac{44}{19} e^{3} + \frac{173}{19} e^{2} + \frac{325}{19} e - \frac{351}{19}$ |
| 73 | $[73, 73, -2 w^{4} + 2 w^{3} + 9 w^{2} - 5 w - 6]$ | $\phantom{-}\frac{10}{19} e^{4} + \frac{26}{19} e^{3} - \frac{110}{19} e^{2} - \frac{129}{19} e + \frac{134}{19}$ |
| 81 | $[81, 3, -2 w^{4} + 3 w^{3} + 10 w^{2} - 9 w - 10]$ | $-\frac{5}{19} e^{4} - \frac{13}{19} e^{3} + \frac{55}{19} e^{2} - \frac{2}{19} e - \frac{67}{19}$ |
| 97 | $[97, 97, -2 w^{4} + 3 w^{3} + 7 w^{2} - 5 w - 4]$ | $\phantom{-}\frac{18}{19} e^{4} + \frac{62}{19} e^{3} - \frac{217}{19} e^{2} - \frac{559}{19} e + \frac{226}{19}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53, 53, -w^{4} + w^{3} + 4 w^{2} - w - 4]$ | $1$ |