Base field 4.4.17989.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[15, 15, -w^{3} + 2w^{2} + 5w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 18x^{2} - 21x + 20\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $-1$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $-1$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}\frac{4}{17}e^{3} - \frac{3}{17}e^{2} - \frac{71}{17}e - \frac{32}{17}$ |
| 16 | $[16, 2, 2]$ | $-\frac{2}{17}e^{3} - \frac{7}{17}e^{2} + \frac{44}{17}e + \frac{101}{17}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{3}{17}e^{3} + \frac{2}{17}e^{2} - \frac{49}{17}e - \frac{58}{17}$ |
| 17 | $[17, 17, -w^{2} + 2w + 3]$ | $-e$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}\frac{7}{17}e^{3} - \frac{1}{17}e^{2} - \frac{103}{17}e - \frac{22}{17}$ |
| 27 | $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ | $\phantom{-}\frac{2}{17}e^{3} + \frac{7}{17}e^{2} - \frac{10}{17}e - \frac{84}{17}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ | $\phantom{-}\frac{3}{17}e^{3} + \frac{2}{17}e^{2} - \frac{32}{17}e - \frac{58}{17}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ | $\phantom{-}\frac{4}{17}e^{3} - \frac{3}{17}e^{2} - \frac{54}{17}e + \frac{2}{17}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}\frac{1}{17}e^{3} + \frac{12}{17}e^{2} - \frac{22}{17}e - \frac{42}{17}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}\frac{5}{17}e^{3} + \frac{9}{17}e^{2} - \frac{76}{17}e - \frac{40}{17}$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{10}{17}e^{3} + \frac{1}{17}e^{2} - \frac{152}{17}e - \frac{80}{17}$ |
| 37 | $[37, 37, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}\frac{7}{17}e^{3} - \frac{1}{17}e^{2} - \frac{69}{17}e - \frac{22}{17}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{1}{17}e^{3} + \frac{5}{17}e^{2} + \frac{5}{17}e - \frac{60}{17}$ |
| 71 | $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}\frac{4}{17}e^{3} - \frac{3}{17}e^{2} - \frac{71}{17}e + \frac{138}{17}$ |
| 71 | $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ | $-\frac{5}{17}e^{3} - \frac{9}{17}e^{2} + \frac{127}{17}e + \frac{142}{17}$ |
| 89 | $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ | $\phantom{-}\frac{11}{17}e^{3} - \frac{21}{17}e^{2} - \frac{174}{17}e + \frac{116}{17}$ |
| 97 | $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{10}{17}e^{3} + \frac{16}{17}e^{2} + \frac{169}{17}e - \frac{124}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $1$ |
| $5$ | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $1$ |