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: | $5$ |
| 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:
| \(x^{5} - 6x^{4} - 9x^{3} + 75x^{2} - 27x - 92\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}\frac{18}{269}e^{4} - \frac{58}{269}e^{3} - \frac{353}{269}e^{2} + \frac{489}{269}e + \frac{1500}{269}$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{269}e^{4} + \frac{63}{269}e^{3} - \frac{85}{269}e^{2} - \frac{879}{269}e + \frac{365}{269}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{32}{269}e^{4} + \frac{133}{269}e^{3} + \frac{508}{269}e^{2} - \frac{1497}{269}e - \frac{694}{269}$ |
| 17 | $[17, 17, -w^{2} + 2w + 3]$ | $-\frac{9}{269}e^{4} + \frac{29}{269}e^{3} + \frac{42}{269}e^{2} - \frac{110}{269}e + \frac{326}{269}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{59}{269}e^{4} + \frac{220}{269}e^{3} + \frac{903}{269}e^{2} - \frac{2096}{269}e - \frac{1330}{269}$ |
| 27 | $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ | $\phantom{-}\frac{18}{269}e^{4} - \frac{58}{269}e^{3} - \frac{353}{269}e^{2} + \frac{758}{269}e + \frac{2038}{269}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ | $-\frac{32}{269}e^{4} + \frac{133}{269}e^{3} + \frac{508}{269}e^{2} - \frac{1228}{269}e - \frac{694}{269}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ | $-\frac{18}{269}e^{4} + \frac{58}{269}e^{3} + \frac{353}{269}e^{2} - \frac{758}{269}e - \frac{1500}{269}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}\frac{32}{269}e^{4} - \frac{133}{269}e^{3} - \frac{508}{269}e^{2} + \frac{1228}{269}e + \frac{1770}{269}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}\frac{50}{269}e^{4} - \frac{191}{269}e^{3} - \frac{861}{269}e^{2} + \frac{1448}{269}e + \frac{2732}{269}$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $-\frac{18}{269}e^{4} + \frac{58}{269}e^{3} + \frac{353}{269}e^{2} - \frac{758}{269}e - \frac{1500}{269}$ |
| 37 | $[37, 37, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}\frac{14}{269}e^{4} - \frac{75}{269}e^{3} - \frac{155}{269}e^{2} + \frac{1277}{269}e - \frac{806}{269}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{41}{269}e^{4} + \frac{162}{269}e^{3} + \frac{819}{269}e^{2} - \frac{1876}{269}e - \frac{2520}{269}$ |
| 71 | $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}\frac{64}{269}e^{4} - \frac{266}{269}e^{3} - \frac{747}{269}e^{2} + \frac{2187}{269}e + \frac{1388}{269}$ |
| 71 | $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ | $-\frac{23}{269}e^{4} + \frac{104}{269}e^{3} + \frac{197}{269}e^{2} - \frac{580}{269}e + \frac{594}{269}$ |
| 89 | $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ | $\phantom{-}\frac{13}{269}e^{4} - \frac{12}{269}e^{3} - \frac{509}{269}e^{2} + \frac{129}{269}e + \frac{4132}{269}$ |
| 97 | $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}\frac{2}{269}e^{4} - \frac{126}{269}e^{3} + \frac{170}{269}e^{2} + \frac{2027}{269}e + \frac{346}{269}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $-1$ |
| $5$ | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $-1$ |