Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 6x^{5} - 15x^{4} - 100x^{3} + 128x^{2} + 472x - 667\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{3} + 8w + 8]$ | $-e - 2$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{5}{7}e^{4} - \frac{6}{7}e^{3} - \frac{38}{7}e^{2} + \frac{5}{7}e + \frac{40}{7}$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $-\frac{1}{7}e^{5} - \frac{5}{7}e^{4} + \frac{13}{7}e^{3} + \frac{59}{7}e^{2} - \frac{61}{7}e - \frac{124}{7}$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{5}{7}e^{4} - \frac{13}{7}e^{3} - \frac{59}{7}e^{2} + \frac{61}{7}e + \frac{82}{7}$ |
| 19 | $[19, 19, -w + 2]$ | $-\frac{1}{7}e^{5} - \frac{5}{7}e^{4} + \frac{6}{7}e^{3} + \frac{38}{7}e^{2} - \frac{5}{7}e - \frac{26}{7}$ |
| 25 | $[25, 5, 2w^{2} - 2w - 13]$ | $-e^{2} - 2e + 6$ |
| 29 | $[29, 29, -w^{2} + 9]$ | $-\frac{1}{7}e^{5} - \frac{12}{7}e^{4} - \frac{22}{7}e^{3} + \frac{143}{7}e^{2} + \frac{254}{7}e - \frac{642}{7}$ |
| 29 | $[29, 29, -w^{2} + 2w + 6]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{15}{7}e^{3} - \frac{157}{7}e^{2} - \frac{198}{7}e + \frac{635}{7}$ |
| 29 | $[29, 29, w^{2} - 7]$ | $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{41}{7}e^{3} - \frac{39}{7}e^{2} - \frac{306}{7}e + \frac{443}{7}$ |
| 29 | $[29, 29, -w^{2} + 2w + 8]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - \frac{34}{7}e^{3} + \frac{67}{7}e^{2} + \frac{278}{7}e - \frac{562}{7}$ |
| 31 | $[31, 31, -2w^{2} + w + 12]$ | $-\frac{2}{7}e^{5} - \frac{10}{7}e^{4} + \frac{19}{7}e^{3} + \frac{104}{7}e^{2} - \frac{59}{7}e - \frac{206}{7}$ |
| 31 | $[31, 31, 2w^{2} - 3w - 11]$ | $\phantom{-}\frac{2}{7}e^{5} + \frac{10}{7}e^{4} - \frac{19}{7}e^{3} - \frac{90}{7}e^{2} + \frac{87}{7}e + \frac{80}{7}$ |
| 41 | $[41, 41, -w]$ | $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - \frac{34}{7}e^{3} + \frac{60}{7}e^{2} + \frac{257}{7}e - \frac{492}{7}$ |
| 41 | $[41, 41, -w + 1]$ | $-\frac{1}{7}e^{5} - \frac{12}{7}e^{4} - \frac{22}{7}e^{3} + \frac{136}{7}e^{2} + \frac{247}{7}e - \frac{558}{7}$ |
| 49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{34}{7}e^{3} - \frac{60}{7}e^{2} - \frac{264}{7}e + \frac{478}{7}$ |
| 49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{22}{7}e^{3} - \frac{136}{7}e^{2} - \frac{240}{7}e + \frac{558}{7}$ |
| 61 | $[61, 61, 2w^{2} - 3w - 14]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{22}{7}e^{3} - \frac{157}{7}e^{2} - \frac{275}{7}e + \frac{789}{7}$ |
| 61 | $[61, 61, 2w^{2} - w - 15]$ | $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{34}{7}e^{3} - \frac{81}{7}e^{2} - \frac{313}{7}e + \frac{695}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $-1$ |