Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[14, 14, -w^{3} - w^{2} + 6w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 6x^{6} - 5x^{5} + 79x^{4} - 91x^{3} - 82x^{2} + 76x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $-1$ |
| 5 | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + 6w - 2]$ | $-1$ |
| 8 | $[8, 2, w^{3} - 7w + 3]$ | $\phantom{-}\frac{1}{24}e^{6} - \frac{7}{8}e^{4} - \frac{7}{24}e^{3} + \frac{115}{24}e^{2} + \frac{8}{3}e - \frac{23}{6}$ |
| 11 | $[11, 11, -w^{3} + 6w - 4]$ | $\phantom{-}\frac{1}{6}e^{5} - \frac{2}{3}e^{4} - \frac{11}{6}e^{3} + \frac{49}{6}e^{2} - \frac{3}{2}e - \frac{13}{3}$ |
| 17 | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $\phantom{-}\frac{1}{12}e^{6} - \frac{2}{3}e^{5} - \frac{1}{12}e^{4} + \frac{35}{4}e^{3} - \frac{133}{12}e^{2} - \frac{26}{3}e + \frac{17}{3}$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{2}{3}e^{5} - \frac{23}{24}e^{4} + \frac{203}{24}e^{3} - \frac{175}{24}e^{2} - 5e + \frac{29}{6}$ |
| 31 | $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ | $-\frac{13}{24}e^{6} + \frac{8}{3}e^{5} + \frac{113}{24}e^{4} - \frac{853}{24}e^{3} + \frac{187}{8}e^{2} + \frac{127}{3}e - \frac{29}{2}$ |
| 37 | $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ | $\phantom{-}\frac{1}{12}e^{6} - \frac{2}{3}e^{5} - \frac{1}{12}e^{4} + \frac{39}{4}e^{3} - \frac{133}{12}e^{2} - \frac{59}{3}e + \frac{11}{3}$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $-\frac{1}{12}e^{6} + \frac{1}{6}e^{5} + \frac{13}{12}e^{4} - \frac{5}{4}e^{3} - \frac{5}{12}e^{2} - \frac{53}{6}e - \frac{2}{3}$ |
| 47 | $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ | $-\frac{1}{2}e^{6} + \frac{5}{2}e^{5} + \frac{9}{2}e^{4} - 34e^{3} + 20e^{2} + \frac{97}{2}e - 17$ |
| 47 | $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ | $-\frac{1}{24}e^{6} + \frac{7}{8}e^{4} - \frac{17}{24}e^{3} - \frac{91}{24}e^{2} + \frac{22}{3}e - \frac{7}{6}$ |
| 59 | $[59, 59, -2w^{3} + 13w - 6]$ | $\phantom{-}\frac{1}{6}e^{6} - e^{5} - \frac{1}{2}e^{4} + \frac{77}{6}e^{3} - \frac{113}{6}e^{2} - \frac{34}{3}e + \frac{38}{3}$ |
| 59 | $[59, 59, -w^{3} - w^{2} + 5w + 2]$ | $-2e + 4$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $\phantom{-}\frac{1}{6}e^{6} - e^{5} - \frac{3}{2}e^{4} + \frac{83}{6}e^{3} - \frac{35}{6}e^{2} - \frac{61}{3}e - \frac{4}{3}$ |
| 59 | $[59, 59, w^{2} + 2w - 6]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{2}e^{5} - \frac{13}{8}e^{4} + \frac{53}{8}e^{3} + \frac{15}{8}e^{2} - \frac{17}{2}e - \frac{3}{2}$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 8w - 7]$ | $-\frac{1}{4}e^{6} + \frac{7}{6}e^{5} + \frac{31}{12}e^{4} - \frac{193}{12}e^{3} + \frac{89}{12}e^{2} + \frac{49}{2}e - \frac{40}{3}$ |
| 67 | $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ | $\phantom{-}\frac{1}{6}e^{6} - \frac{5}{6}e^{5} - \frac{7}{6}e^{4} + 11e^{3} - \frac{32}{3}e^{2} - \frac{77}{6}e + \frac{37}{3}$ |
| 73 | $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ | $-\frac{1}{8}e^{6} + \frac{1}{3}e^{5} + \frac{55}{24}e^{4} - \frac{115}{24}e^{3} - \frac{265}{24}e^{2} + 11e + \frac{59}{6}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{12}e^{6} + \frac{1}{6}e^{5} - \frac{29}{12}e^{4} - \frac{29}{12}e^{3} + \frac{67}{4}e^{2} + \frac{23}{6}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 1]$ | $1$ |
| $7$ | $[7, 7, -w^{3} + 6w - 2]$ | $1$ |