Base field 4.4.10309.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 8x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 7x^{6} - 39x^{5} + 228x^{4} + 796x^{3} - 1783x^{2} - 7800x - 6452\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, w^{3} - 5w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 5w + 2]$ | $-\frac{1}{6}e^{6} + \frac{13}{12}e^{5} + \frac{31}{6}e^{4} - \frac{359}{12}e^{3} - \frac{275}{4}e^{2} + \frac{2405}{12}e + \frac{2285}{6}$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{1}{3}e^{6} + \frac{41}{12}e^{5} + \frac{19}{3}e^{4} - \frac{1321}{12}e^{3} - \frac{353}{4}e^{2} + \frac{12469}{12}e + \frac{9097}{6}$ |
| 13 | $[13, 13, w^{3} - 6w + 4]$ | $-\frac{1}{3}e^{6} + \frac{41}{12}e^{5} + \frac{19}{3}e^{4} - \frac{1321}{12}e^{3} - \frac{353}{4}e^{2} + \frac{12469}{12}e + \frac{9097}{6}$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 17 | $[17, 17, w^{2} + w - 2]$ | $-\frac{5}{8}e^{6} + \frac{11}{2}e^{5} + \frac{117}{8}e^{4} - \frac{1357}{8}e^{3} - \frac{1585}{8}e^{2} + \frac{5939}{4}e + 2293$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $-\frac{5}{8}e^{6} + \frac{11}{2}e^{5} + \frac{117}{8}e^{4} - \frac{1357}{8}e^{3} - \frac{1585}{8}e^{2} + \frac{5939}{4}e + 2293$ |
| 23 | $[23, 23, w^{3} - w^{2} - 6w + 6]$ | $\phantom{-}\frac{31}{24}e^{6} - \frac{139}{12}e^{5} - \frac{703}{24}e^{4} + \frac{8569}{24}e^{3} + \frac{3163}{8}e^{2} - \frac{18805}{6}e - \frac{28685}{6}$ |
| 23 | $[23, 23, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}\frac{31}{24}e^{6} - \frac{139}{12}e^{5} - \frac{703}{24}e^{4} + \frac{8569}{24}e^{3} + \frac{3163}{8}e^{2} - \frac{18805}{6}e - \frac{28685}{6}$ |
| 25 | $[25, 5, -w^{2} + 3]$ | $-\frac{17}{12}e^{6} + \frac{37}{3}e^{5} + \frac{401}{12}e^{4} - \frac{4529}{12}e^{3} - \frac{1803}{4}e^{2} + \frac{19573}{6}e + \frac{15139}{3}$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 5w + 1]$ | $-\frac{17}{12}e^{6} + \frac{37}{3}e^{5} + \frac{401}{12}e^{4} - \frac{4529}{12}e^{3} - \frac{1803}{4}e^{2} + \frac{19573}{6}e + \frac{15139}{3}$ |
| 29 | $[29, 29, -w^{2} - 2w + 3]$ | $-\frac{37}{24}e^{6} + \frac{40}{3}e^{5} + \frac{877}{24}e^{4} - \frac{9769}{24}e^{3} - \frac{3935}{8}e^{2} + \frac{42101}{12}e + \frac{16327}{3}$ |
| 29 | $[29, 29, -w^{3} + w^{2} + 7w - 7]$ | $-\frac{37}{24}e^{6} + \frac{40}{3}e^{5} + \frac{877}{24}e^{4} - \frac{9769}{24}e^{3} - \frac{3935}{8}e^{2} + \frac{42101}{12}e + \frac{16327}{3}$ |
| 43 | $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ | $\phantom{-}\frac{1}{24}e^{6} - \frac{1}{3}e^{5} - \frac{25}{24}e^{4} + \frac{253}{24}e^{3} + \frac{99}{8}e^{2} - \frac{1145}{12}e - \frac{406}{3}$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 5w - 7]$ | $\phantom{-}\frac{1}{24}e^{6} - \frac{1}{3}e^{5} - \frac{25}{24}e^{4} + \frac{253}{24}e^{3} + \frac{99}{8}e^{2} - \frac{1145}{12}e - \frac{406}{3}$ |
| 53 | $[53, 53, w^{3} - w^{2} - 7w + 5]$ | $-\frac{11}{24}e^{6} + \frac{41}{12}e^{5} + \frac{299}{24}e^{4} - \frac{2345}{24}e^{3} - \frac{1307}{8}e^{2} + \frac{2206}{3}e + \frac{7363}{6}$ |
| 53 | $[53, 53, w^{2} + 2w - 5]$ | $-\frac{11}{24}e^{6} + \frac{41}{12}e^{5} + \frac{299}{24}e^{4} - \frac{2345}{24}e^{3} - \frac{1307}{8}e^{2} + \frac{2206}{3}e + \frac{7363}{6}$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 10w]$ | $-\frac{17}{12}e^{6} + \frac{40}{3}e^{5} + \frac{365}{12}e^{4} - \frac{5033}{12}e^{3} - \frac{1663}{4}e^{2} + \frac{22843}{6}e + \frac{17158}{3}$ |
| 61 | $[61, 61, w^{3} - 7w + 3]$ | $\phantom{-}\frac{35}{24}e^{6} - \frac{155}{12}e^{5} - \frac{803}{24}e^{4} + \frac{9533}{24}e^{3} + \frac{3591}{8}e^{2} - \frac{20855}{6}e - \frac{31885}{6}$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ | $-\frac{17}{12}e^{6} + \frac{40}{3}e^{5} + \frac{365}{12}e^{4} - \frac{5033}{12}e^{3} - \frac{1663}{4}e^{2} + \frac{22843}{6}e + \frac{17158}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |