Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, 6w - 35]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - x^{5} - 9x^{4} + 9x^{3} + 14x^{2} - 9x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 5]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{2}{7}e^{4} - \frac{10}{7}e^{3} - 2e^{2} + 3e + \frac{12}{7}$ |
| 7 | $[7, 7, 6w - 35]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -6w - 29]$ | $-\frac{2}{7}e^{5} + \frac{3}{7}e^{4} + \frac{20}{7}e^{3} - 3e^{2} - 6e - \frac{3}{7}$ |
| 9 | $[9, 3, 3]$ | $-\frac{3}{7}e^{5} + \frac{1}{7}e^{4} + \frac{23}{7}e^{3} - 2e^{2} - 4e + \frac{13}{7}$ |
| 11 | $[11, 11, 4w + 19]$ | $-\frac{2}{7}e^{5} - \frac{4}{7}e^{4} + \frac{20}{7}e^{3} + 4e^{2} - 7e - \frac{24}{7}$ |
| 11 | $[11, 11, 4w - 23]$ | $-\frac{4}{7}e^{5} - \frac{1}{7}e^{4} + \frac{33}{7}e^{3} - 5e - \frac{6}{7}$ |
| 13 | $[13, 13, -2w + 11]$ | $-\frac{2}{7}e^{5} + \frac{3}{7}e^{4} + \frac{20}{7}e^{3} - 4e^{2} - 6e + \frac{18}{7}$ |
| 13 | $[13, 13, 2w + 9]$ | $\phantom{-}\frac{4}{7}e^{5} - \frac{6}{7}e^{4} - \frac{33}{7}e^{3} + 7e^{2} + 4e - \frac{36}{7}$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{8}{7}e^{5} - \frac{5}{7}e^{4} - \frac{73}{7}e^{3} + 6e^{2} + 17e - \frac{51}{7}$ |
| 31 | $[31, 31, 2w - 13]$ | $-\frac{4}{7}e^{5} + \frac{6}{7}e^{4} + \frac{40}{7}e^{3} - 8e^{2} - 11e + \frac{43}{7}$ |
| 31 | $[31, 31, -2w - 11]$ | $-e^{2} + e + 1$ |
| 41 | $[41, 41, -8w - 39]$ | $\phantom{-}\frac{12}{7}e^{5} + \frac{3}{7}e^{4} - \frac{106}{7}e^{3} + 25e - \frac{31}{7}$ |
| 41 | $[41, 41, 8w - 47]$ | $\phantom{-}\frac{5}{7}e^{5} - \frac{4}{7}e^{4} - \frac{57}{7}e^{3} + 7e^{2} + 21e - \frac{66}{7}$ |
| 53 | $[53, 53, -26w - 125]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{2}{7}e^{4} - \frac{10}{7}e^{3} - e^{2} + 4e - \frac{37}{7}$ |
| 53 | $[53, 53, 26w - 151]$ | $-\frac{3}{7}e^{5} + \frac{1}{7}e^{4} + \frac{37}{7}e^{3} - 14e - \frac{43}{7}$ |
| 61 | $[61, 61, -14w + 81]$ | $\phantom{-}e^{5} - 10e^{3} + e^{2} + 21e - 4$ |
| 61 | $[61, 61, -14w - 67]$ | $\phantom{-}e^{4} - 7e^{2} + 6e + 4$ |
| 83 | $[83, 83, 2w - 15]$ | $-\frac{19}{7}e^{5} + \frac{11}{7}e^{4} + \frac{162}{7}e^{3} - 15e^{2} - 30e + \frac{52}{7}$ |
| 83 | $[83, 83, -2w - 13]$ | $-\frac{5}{7}e^{5} + \frac{4}{7}e^{4} + \frac{57}{7}e^{3} - 3e^{2} - 23e - \frac{4}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, 6w - 35]$ | $-1$ |