Base field 4.4.19429.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[15, 15, w^{2} - 2w - 5]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 3x^{5} - 12x^{4} + 15x^{3} + 38x^{2} + 14x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w]$ | $-1$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-e^{5} + 3e^{4} + 12e^{3} - 16e^{2} - 36e - 9$ |
| 13 | $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}e^{2} - 2e - 5$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{4}{3}e^{5} - \frac{14}{3}e^{4} - \frac{41}{3}e^{3} + \frac{79}{3}e^{2} + 38e + \frac{11}{3}$ |
| 17 | $[17, 17, -w + 2]$ | $-\frac{5}{3}e^{5} + \frac{16}{3}e^{4} + \frac{58}{3}e^{3} - \frac{89}{3}e^{2} - 61e - \frac{34}{3}$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{7}{3}e^{5} - \frac{23}{3}e^{4} - \frac{77}{3}e^{3} + \frac{124}{3}e^{2} + 76e + \frac{41}{3}$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ | $-2e^{5} + 7e^{4} + 20e^{3} - 39e^{2} - 52e - 4$ |
| 31 | $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}e^{5} - 3e^{4} - 13e^{3} + 18e^{2} + 44e + 6$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{4}{3}e^{5} + \frac{14}{3}e^{4} + \frac{41}{3}e^{3} - \frac{79}{3}e^{2} - 40e - \frac{17}{3}$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}2e^{5} - 6e^{4} - 24e^{3} + 31e^{2} + 73e + 19$ |
| 43 | $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ | $-\frac{8}{3}e^{5} + \frac{25}{3}e^{4} + \frac{94}{3}e^{3} - \frac{137}{3}e^{2} - 96e - \frac{52}{3}$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}e^{5} - 3e^{4} - 12e^{3} + 16e^{2} + 39e + 1$ |
| 53 | $[53, 53, -w - 3]$ | $-\frac{1}{3}e^{5} + \frac{2}{3}e^{4} + \frac{17}{3}e^{3} - \frac{13}{3}e^{2} - 22e - \frac{11}{3}$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ | $\phantom{-}e^{5} - 3e^{4} - 12e^{3} + 15e^{2} + 38e + 12$ |
| 59 | $[59, 59, 2w^{2} - 3w - 6]$ | $\phantom{-}\frac{8}{3}e^{5} - \frac{28}{3}e^{4} - \frac{82}{3}e^{3} + \frac{161}{3}e^{2} + 71e + \frac{7}{3}$ |
| 59 | $[59, 59, w^{3} - w^{2} - 7w - 3]$ | $-\frac{1}{3}e^{5} + \frac{5}{3}e^{4} + \frac{5}{3}e^{3} - \frac{34}{3}e^{2} + \frac{7}{3}$ |
| 79 | $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ | $\phantom{-}\frac{5}{3}e^{5} - \frac{16}{3}e^{4} - \frac{55}{3}e^{3} + \frac{83}{3}e^{2} + 52e + \frac{31}{3}$ |
| 79 | $[79, 79, w^{2} - 2w - 1]$ | $\phantom{-}\frac{11}{3}e^{5} - \frac{37}{3}e^{4} - \frac{115}{3}e^{3} + \frac{197}{3}e^{2} + 106e + \frac{61}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $-1$ |
| $5$ | $[5, 5, w]$ | $1$ |